Gregor Johann Mendel is known as the Father of Genetics.

A trait is a specific characteristic of an organism, such as height, eye colour, or skin colour.

A monohybrid cross involves only one pair of contrasting characters, such as tall vs. dwarf in pea plants.

The 3:1 ratio represents 3 offspring with the dominant phenotype to 1 with the recessive phenotype in F2.

DNA fingerprinting is used in forensic science (criminal investigation).

The gene is the basic unit of heredity.

Genetic engineering modifies an organism's DNA by adding, deleting, or substituting specific genes to produce new or improved traits.

Siblings look different because meiosis and crossing over produce unique allele combinations in each gamete before fertilisation.

Human cloning and modification of the human genome is a major ethical concern related to genetic modification.

Pea plants have many clearly contrasting traits (e.g., tall/dwarf, round/wrinkled seeds) that are easy to observe.

They can be self-pollinated or cross-pollinated easily in controlled experiments.

Phenotypic ratio (F2): Tall : Dwarf = 3 : 1

Genotypic ratio (F2): TT : Tt : tt = 1 : 2 : 1

Transgenic crops resist pests, diseases, and harsh conditions and improving yield.

Molecular markers help select plants with desired traits like high yield or drought tolerance.

DNA is extracted from biological evidence (blood, hair, saliva) at the crime scene and a unique DNA profile is created. This is compared with a suspect's DNA for a match.

a. What type of cross is this?

a) This is a monohybrid cross — between two hybrid parents (Rr × Rr) involving one pair of contrasting characters.

b. Which filial generation is shown in the given picture?

b) This is the F2 generation, produced by crossing two F1 hybrid plants, giving the 1:2:1 genotypic ratio.

The Law of Segregation states that the dominant and recessive characters of the hybrids separate during the gamete formation in such a way that each gamete receives only one character at a time. Example: hybrid tall plant (Tt) → gametes T and t — each pure, never mixed.

Gene therapy identifies and corrects defective genes to treat hereditary disorders.

Recombinant DNA technology produces human proteins and vaccines.

GM crops resist pests, diseases, and harsh conditions, reducing crop losses. They also decrease dependence on chemical pesticides, lowering production costs and environmental damage.

Plants: A pea plant inheriting two dominant tall alleles (TT) will always be tall — heredity directly determines plant height.

Humans: A child born to two brown-eyed parents is likely to have brown eyes, as the dominant brown allele is inherited through chromosomes.

Conclusions:

Law of Dominance: T completely masks t in F1.

Law of Segregation: Alleles separate during gamete formation; each gamete carries only one allele.

Genotype vs Phenotype: A hybrid Tt looks tall but carries a hidden recessive allele t.

Recessive traits disappear in F1 but reappear in 1/4 of F2 offspring.

Law of Dominance: When pure-breeding plants with contrasting traits are crossed, only the dominant trait appears in F1. Example: TT × tt → all Tt (all tall). In F2 (Tt × Tt): 3 tall : 1 dwarf — dominant (T) always masks recessive (t).

Law of Segregation: During meiosis, the two alleles separate so each gamete carries only one pure allele. Example: Hybrid Tt → gametes T and t (each pure). The reappearance of pure dwarf (tt) in F2 proves that B and t alleles stayed separate inside the F1 hybrid — they never blended.

Phenotypic ratio: Black : White = 1 : 1

Genotypic ratio: Bb : bb = 1 : 1

Agriculture: Transgenic crops resist pests/drought, improving yield.

Medicine: Gene therapy corrects defective genes; recombinant DNA produces insulin, vaccines, etc.

Forensic Science: DNA fingerprinting identifies criminals and confirms parentage in legal cases.

Biotechnology/Research: Leading to new medical discoveries.

Benefits:

Improved crop yield and food security through transgenic crops.

Medical treatments — gene therapy, insulin, vaccines via recombinant DNA technology.

DNA fingerprinting aids forensic justice and disaster victim identification.

Early disease detection through genetic testing enables preventive treatment.

Ethical Concerns:

Possible long-term health risks from consuming GM foods.

GMO organisms may disturb natural ecosystems and reduce biodiversity.

Human cloning and designer babies raise serious ethical debates.

Genetic databases risk individual privacy if misused.

Genes are passed through chromosomes — children inherit traits like eye colour and height from parents. However, during meiosis, crossing over and random gamete fusion produce unique allele combinations in each child.

Examples: Siblings may have different eye colours or hair types despite the same parents. Similarly, In pea plants, F2 (Tt × Tt) produces both tall and dwarf offspring (3:1) — traits are inherited but variation occurs.

He applied mathematics to biology, identifying the 3:1 and 1:2:1 ratios — proving inheritance follows predictable patterns.

He proved traits are controlled by discrete units (genes/alleles), disproving the blending theory of inheritance.

Law of Dominance explains why dominant traits mask recessive ones in offspring.

Law of Segregation shows alleles separate during gamete formation, preserving their identity across generations.

His work led scientists to discover chromosomes and DNA, laying the foundation of all modern molecular genetics.

a. Draw and label the genetic cross.

b. Predict the phenotypic ratio in F2 generation.

Phenotypic ratio: 3 Black : 1 White

c. Explain how this diagram supports Mendel’s Law of Segregation.

The reappearance of pure white (bb) in F2 proves B and b alleles were preserved separately inside the F1 hybrid (Bb) — they never blended. During meiosis, they segregated into separate gametes.

This process is called Genetic Engineering .

b. Predict one benefit and one possible risk of this technology.

One Benefit: Inserting the human insulin gene into bacteria allows mass production of affordable insulin for treating diabetes.

One Risk: Possible long-term health risks from GM foods.

c. Suggest an example where such modification can be used for human welfare.

Inserting the Bt-toxin gene from Bacillus thuringiensis into crop plants creates pest-resistant transgenic crops that protect yields without harmful chemical pesticides.

a. If the pattern of Lane 1 matches Lane 3, what conclusion can be drawn?

Suspect B was present at the crime scene — DNA bands match exactly. Every person has a unique DNA pattern, making this strong evidence.

b. What scientific principle allows each person to have a unique DNA pattern?

The nucleotide sequence of DNA is unique to each individual. DNA fingerprinting targets highly variable regions of the genome that differ between people.

c. How can this technique also be applied in paternity testing or disaster identification?

Paternity Testing: Child's DNA bands are compared to the alleged father — shared bands confirm biological parenthood. Disaster Identification: DNA from remains is compared to relatives' DNA to identify victims.

a. What type of trait (dominant or recessive) does “dimple” represent?

Dimples represent a dominant trait (it appears in every generation where at least one parent carries it)

b. Draw a simple chart to represent this inheritance pattern.

c. How can you use this family data to predict traits in the next generation?

Half of the next generation will have dimples.

Identify the genotype and phenotype ratios of the offspring.

If “T” represents tallness, explain why all plants in F1 generation are tall.

All F1 plants are tall because T (tallness) is dominant. Both TT and Tt appear tall.

How does this diagram support Mendel’s Law of Dominance?

T always expresses tallness, confirming dominant allele suppresses recessive.

The left ventricle pumps oxygenated blood to the entire body via the aorta (systemic circulation), requiring much greater force than the right ventricle, which only pumps blood to the nearby lungs.

Unlike all other veins which carry deoxygenated blood, pulmonary veins carry oxygenated blood from the lungs back to the left atrium.

During exercise, muscles need more oxygen and produce more CO₂, so the brain signals the heart to beat faster to deliver oxygen and remove waste gases quickly.

150/95 mmHg exceeds the normal range and indicates hypertension (high blood pressure).

Increased WBC count shows the immune system is producing more white blood cells to fight the infection through phagocytosis and antibody production.

Incompatible blood causes agglutination (clumping) of red blood cells that can block blood vessels and cause life-threatening reactions.

Platelets gather at the wound and release chemicals that convert fibrinogen into fibrin threads, forming a clot that seals the wound.

Regular exercise strengthens the heart muscle, reduces blood pressure, lowers cholesterol, and maintains a healthy body weight.

More RBCs provide more haemoglobin to bind the limited oxygen at high altitude, ensuring adequate oxygen supply to muscles and organs.

Pulmonary artery: carries deoxygenated blood from right ventricle to lungs. Pulmonary vein: carries oxygenated blood from lungs back to left atrium.

Right Ventricle → Pulmonary Artery → Lungs (gas exchange) → Pulmonary Veins → Left Atrium.

(i) Pulmonary: Right ventricle → Lungs → Left atrium — oxygenates the blood (CO₂ released, O₂ absorbed).

(ii) Systemic: Left ventricle → Body → Right atrium — delivers oxygen and nutrients to all cells; collects CO₂ and waste.

Double circulation keeps oxygenated and deoxygenated blood completely separate (by the septum), ensuring all tissues receive fully oxygenated blood. It also allows high-pressure delivery to the body while maintaining gentle pressure in the delicate lung capillaries — making the system highly efficient.

The left ventricle pumps oxygenated blood through the entire body via the aorta, requiring much greater pressure. The right ventricle only pumps blood the shorter distance to the nearby lungs and needs far less force.

When a cut occurs, platelets migrate to the wound and release chemicals that convert fibrinogen into insoluble fibrin threads. These form a mesh trapping red blood cells, creating a firm clot that seals the vessel and stops bleeding.

RBCs contain haemoglobin which transports oxygen from the lungs to all tissues. In anaemia, reduced RBCs or haemoglobin means less oxygen reaches cells, so cells cannot produce enough energy, resulting in persistent weakness and fatigue.

Intense exercise makes muscles consume more O₂ and produce more CO₂. The body detects this and signals the heart to beat faster, increasing blood flow per minute to deliver more oxygen to working muscles and remove CO₂ quickly.

18,000/mm³ is above the normal range (4,000–11,000/mm³), indicating leucocytosis — the body is producing extra WBCs (through phagocytosis and antibody production) to fight the infection.

Pallor: Fewer RBCs/haemoglobin means less red pigment, making skin, lips, and gums appear pale. Tiredness: Less oxygen reaches tissues, cells cannot produce sufficient energy through cellular respiration, causing persistent fatigue.

a. Which stage of heart is shown in the figure, systolic or diastolic?

Ventricles contracting and pushing blood out -Systolic stage (systole).

b. Write a important function of heart in this condition.

Right ventricle pumps deoxygenated blood to lungs via pulmonary artery; simultaneously left ventricle pumps oxygenated blood to the entire body via the aorta.

Condition: Thrombocytopenia — impaired blood clotting due to low platelet count.

Primary Risk: Excessive, uncontrolled bleeding — even minor cuts cause prolonged bleeding; spontaneous internal bleeding may also occur.

Precautions:

Avoid high-risk activities (contact sports, sharp tools) to prevent cuts and bruises.

Seek immediate medical attention for any wound bleeding abnormally long.

Avoid aspirin/ibuprofen which further inhibit platelet function.

Eat foods rich in Vitamin K and B12 to support platelet production.

Right Atrium: Receives deoxygenated blood from the entire body via vena cavae; pushes it through the tricuspid valve into the right ventricle.

Right Ventricle: Pumps deoxygenated blood through the pulmonary valve into the pulmonary artery → to lungs for oxygenation. (Only artery carrying deoxygenated blood.)

Left Atrium: Receives oxygenated blood from lungs via pulmonary veins; pushes it through the bicuspid (mitral) valve into the left ventricle. (Only veins carrying oxygenated blood.)

Left Ventricle: Has thickest walls; pumps oxygenated blood through the aortic valve into the aorta for the entire body (systemic circulation).

Septum: Separates right and left sides, preventing mixing of oxygenated and deoxygenated blood.

(i) Arteries — Structure: Thick, strong, elastic walls; narrow lumen (withstands high pressure). Function: Carry oxygenated blood away from heart under high pressure. Exception: pulmonary artery carries deoxygenated blood.

(ii) Veins — Structure: Thinner walls; wide lumen; valves prevent backflow. Function: Carry deoxygenated blood back to heart under low pressure. Exception: pulmonary veins carry oxygenated blood.

(iii) Capillaries — Structure: Walls one cell thick; vast network reaching every tissue. Function: Allow exchange of O₂, nutrients, CO₂, and waste between blood and body cells — actual site of gas exchange.

Double Circulation: Blood passes through the heart TWICE per complete cycle.

Circuit 1 — Pulmonary (Heart ↔ Lungs): Deoxygenated blood → Right Atrium → Right Ventricle → Pulmonary Artery → Lungs (CO₂ released, O₂ absorbed) → Pulmonary Veins → Left Atrium. Purpose: Oxygenate the blood.

Circuit 2 — Systemic (Heart ↔ Body): Left Atrium → Left Ventricle → Aorta → All body parts (O₂ and nutrients delivered, CO₂ collected) → Vena Cavae → Right Atrium. Purpose: Supply oxygen and nutrients to every body cell.

Importance: Keeps oxygenated/deoxygenated blood separate; high-pressure delivery to body; gentle pressure in delicate lung capillaries.

Valves are one-way gates — they open to let blood pass and close to prevent backflow.

Tricuspid Valve (Right atrium → Right ventricle): Opens for filling; closes during RV contraction.

Bicuspid/Mitral Valve (Left atrium → Left ventricle): Same mechanism.

Pulmonary Semilunar Valve (RV → Pulmonary artery): Opens during RV contraction; closes to prevent backflow.

Aortic Semilunar Valve (LV → Aorta): Opens during LV contraction; closes to prevent backflow.

Heart sounds 'lub-dub': 'Lub' = tricuspid/bicuspid valves closing; 'Dub' = semilunar valves closing.

Vasoconstriction: Blood vessels narrow near the wound to slow blood flow.

Platelet Plug: Platelets migrate to the damaged vessel wall, clump together, and release clotting chemicals.

Fibrin Clot: Chemicals convert fibrinogen (plasma protein) into fibrin threads forming a mesh that traps RBCs — creating a firm stable clot.

Healing: Clot hardens into a scab; new skin cells grow beneath it to repair the tissue.

In haemophilia, fibrinogen or clotting factors are absent — this process fails and bleeding continues.

Hypertension: Blood pressure at or above 140/90 mmHg — called the 'silent killer' as it damages heart and blood vessels without obvious symptoms.

Causes: Excess salt/fat intake; physical inactivity; obesity; smoking; excessive alcohol; chronic stress; family history.

Two Preventive Measures:

Eat a low-salt, low-fat diet and exercise regularly — excess salt raises blood pressure by retaining water; exercise strengthens the heart and maintains healthy weight.

Manage stress through yoga or meditation and get regular check-ups — stress raises blood pressure and early detection prevents serious damage.

Reason: Anaemia = deficiency of RBCs or haemoglobin → less oxygen to tissues → insufficient energy production → persistent fatigue and weakness.

Dietary Changes:

Iron-rich foods: spinach, lentils, beans, red meat — iron is essential for haemoglobin production.

Vitamin C (oranges, tomatoes): enhances iron absorption in the intestines.

Vitamin B12 and folate (dairy, eggs, leafy greens): required for RBC production.

Avoid tea/coffee with meals as they inhibit iron absorption.

How: Atherosclerosis (fat/cholesterol plaque) narrows coronary arteries. A ruptured plaque triggers clot formation. Complete blockage cuts off oxygen to the heart muscle, which begins to die (heart attack). Chest pain = oxygen-deprived heart muscle; breathlessness = weakened heart pumps inefficiently.

Prevention:

Avoid smoking and eat a low-fat diet — tobacco damages artery walls; unhealthy fats raise LDL cholesterol, promoting plaque.

Exercise regularly and maintain healthy weight — strengthens heart, reduces blood pressure, and improves cholesterol levels.

A. Chambers: Right Atrium (RA), Right Ventricle (RV), Left Atrium (LA), Left Ventricle (LV). Vessels: Superior/Inferior Vena Cava, Pulmonary Artery, Pulmonary Veins, Aorta.

B. Deoxygenated: Body → Vena Cavae → RA → RV → Pulmonary Artery → Lungs. Oxygenated: Lungs → Pulmonary Veins → LA → LV → Aorta → Body.

C. Efficient O₂ supply: Double circulation separates blood types; strong LV generates high pressure; capillaries allow direct gas exchange; haemoglobin carries 60× more O₂ than plasma alone.

Lifestyle Risks: Stress raises blood pressure; junk food builds plaque (atherosclerosis); inactivity weakens heart and causes obesity; smoking damages artery lining; excess alcohol raises blood pressure.

Four Ways to Maintain Heart Health:

Exercise 30–60 minutes daily — strengthens heart, controls weight, blood pressure, and cholesterol.

Eat a balanced diet — fruits, vegetables, whole grains; limit salt, saturated fats, and sugary foods.

Manage stress — yoga, meditation, or hobbies reduce arterial damage from chronic stress hormones.

Regular health check-ups — monitor blood pressure, blood sugar, and cholesterol for early detection.

A. The Pulmonary Artery carries blood from the right ventricle to the lungs — the only artery carrying deoxygenated blood.

B. C represents the Aorta — carries oxygenated blood from the left ventricle to all parts of the body; the largest artery.

C. Artery (A): thick elastic walls; carries blood away from heart under high pressure. Vein (B): thinner walls with valves; carries blood back to heart under low pressure.

Climate is determined over an average period of 30 years.

Nepal's glaciers, river systems, and diverse geography are extremely sensitive to small temperature changes, causing disproportionate effects like glacial retreat, GLOFs, and drying springs.

Deforestation removes carbon sinks that absorb CO₂ and releases the carbon stored in trees back into the atmosphere, accelerating the greenhouse effect.

GLOFs release massive surges of water and debris, destroying villages, farmland, bridges, and infrastructure downstream.

Climate change warms high-altitude zones and shrinks their habitat; additionally, illegal poaching and depletion of prey species further reduce their population.

Turn off lights and electronics when not in use, walk or cycle for short trips, use public transport, reduce meat consumption, and avoid single-use plastics.

Schools can plant native trees, start recycling programs, run awareness campaigns, participate in reforestation, and educate students about local biodiversity.

Reforest watershed catchment areas, construct rainwater harvesting tanks, and protect spring recharge zones from construction and overgrazing.

Erratic monsoons cause unexpected floods and droughts; rising temperatures spread new pests/diseases; disrupted seasons reduce yields and food security.

Over 22,000 Forest User Groups managing ~2 million hectares have reversed deforestation, regenerated wildlife habitats, reduced erosion, and provided sustainable livelihoods in many areas.

Theme: 'Our Mountains Are Melting — Act Now!' featuring before-and-after glacier images alongside everyday actions like cycling, planting trees, and reducing plastic.

Initially, glacial melt increases river flow, raising flood risk and causing GLOFs that destroy downstream settlements. Long-term, as glaciers shrink, dry-season flows decrease, creating water scarcity for drinking, irrigation, and hydropower — leading to displacement and crop failure.

Every species plays a specific ecological role — pollination, pest control, nutrient cycling, and water purification. Loss of even one species can disrupt food chains; high biodiversity makes ecosystems more resilient to climate shifts and disease.

Switch to LED bulbs and turn off all appliances when not in use — reduces electricity demand and power plant emissions.

Reduce meat consumption by having at least one vegetarian day per week — livestock farming releases significant methane (CH₄).

Establish community forests with protected zones and ban unsustainable commercial harvesting.

Set up local nurseries to cultivate rare plants and educate community members about their ecological and medicinal value.

Plant deep-rooted native trees and grasses on slopes to stabilise soil; construct retaining walls, check dams, and drainage channels.

Implement land-use zoning to avoid construction on unstable slopes, and install early warning systems using rain gauges.

Reusing reduces manufacturing demand and associated CO₂ emissions. Recycling uses far less energy than processing raw materials (e.g., recycling aluminium uses 95% less energy), and both reduce landfill waste which produces methane as organic matter decomposes.

Choose native species suited to local climate and soil — they survive better and support local biodiversity far better than exotic species.

Ensure long-term maintenance through dedicated student groups — plantations without systematic watering and protection have very high sapling mortality.

Erratic monsoon patterns cause both sudden floods and prolonged droughts in the same season, making yields unpredictable.

Rising temperatures expand the range of pests and diseases into previously cooler hill areas, exposing crops to new threats.

In-situ conservation protects entire ecosystems — food chains, migration routes, and ecological relationships — not just individual species. Nepal's protected area network (~23% of land) has successfully increased populations of Bengal tigers and one-horned rhinoceroses, demonstrating this holistic approach is most effective at scale.

'Bring Your Own Bag' campaign with shop discounts for customers using reusable bags — making the sustainable choice economically attractive.

Monthly plastic collection drives with upcycling workshops — repurposing waste into useful items makes conservation engaging and creates economic value.

(a) Greenhouse Gases: CO₂, methane (CH₄), nitrous oxide (N₂O), and water vapour trap outgoing infrared radiation, warming the planet like greenhouse glass. Human activities have raised CO₂ from ~280 ppm (pre-industrial) to over 420 ppm today.

(b) Global Warming: A gradual rise in Earth's average surface temperature due to the enhanced greenhouse effect. Earth has warmed ~1.1°C since pre-industrial times, causing melting glaciers, rising sea levels, and extreme weather. In Nepal, temperatures rise ~0.06°C/year, causing retreating glaciers and erratic monsoons.

(c) Biodiversity: The variety of all living organisms — genetic, species, and ecosystem diversity. Nepal is a global hotspot spanning tropical Terai to alpine Himalayan zones, hosting 700+ medicinal plant species. High biodiversity ensures ecosystem stability and services like clean water, pollination, and soil fertility.

(d) Endangered Species: Organisms whose populations have declined so drastically they face significant extinction risk, classified on the IUCN Red List. Nepal's examples: Snow Leopard, Bengal Tiger, One-horned Rhinoceros, Red Panda, Yarsagumba. Main threats: habitat loss, climate change, poaching, and overexploitation.

Glacial Retreat and GLOFs: Himalayan glaciers retreating rapidly; Imja Glacial Lake has grown dangerously, threatening Solukhumbu villages.

Water Scarcity: Mountain springs and glacier-fed rivers are drying, affecting drinking water, irrigation, and hydropower in hill communities.

Loss of Biodiversity: Snow leopards lose habitat as vegetation zones shift upward; Yarsagumba declines due to warming and overharvesting.

Extreme Weather: Unseasonal rains trigger hill landslides; droughts affect Terai farming; major floods (2017, 2020) displaced thousands.

Human Health: Malaria-carrying mosquitoes spreading into previously cold hill districts; heat strokes increasing in the Terai.

Economic Losses: Annual disasters cost billions in infrastructure damage and agricultural losses, straining Nepal's development.

Protected Area Network (In-situ): 20 national parks, wildlife reserves, and conservation areas covering ~23% of Nepal, protecting tigers, rhinos, elephants, and rare Himalayan flora.

Legal Protection: The Control of International Trade of Endangered Wild Fauna and Flora Act, 2073 prohibits hunting/trading of 27 protected mammal species, 9 bird species, and 3 reptile species with heavy penalties.

Community Forestry Programme: 22,000+ Forest User Groups manage ~2 million hectares, reversing deforestation and protecting biodiversity while providing sustainable livelihoods — internationally recognised.

Ex-situ Conservation: The Central Zoo, Gharial Breeding Centre (Chitwan), and vulture breeding centres breed critically endangered species with reintroduction goals.

A. The picture shows glaciers retreating due to rising temperatures from climate change — bare rock is exposed as the ice mass progressively shrinks.

B. Short-term: increased melt raises river levels and flood risk. Long-term: Nepal's glacier-fed rivers (Koshi, Gandaki, Karnali) lose dry-season flow, threatening irrigation for Terai farmland, hill drinking water, and most of Nepal's hydropower. Crop yields fall as irrigation becomes unreliable.

C. Two measures: (1) Globally reduce greenhouse gas emissions by transitioning to renewable energy — slows glacial melt at its source. (2) Locally, construct GLOF early warning systems and controlled drainage of dangerous glacial lakes to protect downstream communities.

Home — Energy Conservation: Switch off lights, fans, and electronics when not in use; replace incandescent bulbs with LEDs to cut electricity demand and power plant emissions.

School — Reduce Plastic Waste: Carry reusable water bottles and containers; refuse plastic straws; organise 'No Single-Use Plastic' campaigns — plastic production is energy-intensive and landfill plastic produces methane.

Transport — Walk or Cycle: Walk or cycle for trips under 2 km; encourage parents to use public transport — vehicle emissions are a major CO₂ source in urban areas.

Community — Reforestation and Awareness: Participate in tree-planting drives and share climate information through posters and social media — each tree sequesters carbon and restores habitat.

Causes: Deforestation removes trees that recharge groundwater. Erratic/reduced rainfall decreases spring recharge. Overextraction for irrigation lowers water tables. Rising temperatures increase evaporation.

Four Local Measures:

Reforest catchment areas with native trees to intercept rainfall and slowly recharge groundwater.

Construct household and community rainwater harvesting tanks to store monsoon water for dry season use.

Regulate water extraction through rotational household use; avoid year-round water-intensive crops.

Identify and protect spring recharge zones (paani mulas) from construction, overgrazing, and deforestation.

A. Two activities: (1) Industrial pollution — factories releasing smoke/effluents. (2) Deforestation — clearing forests for agriculture or settlements.

B. Industrial pollution introduces toxins making habitats uninhabitable (aquatic life dies from effluents). Deforestation destroys wildlife habitat, fragments ecosystems, prevents migration, and reduces food sources — driving species toward extinction.

C. (1) Enforce environmental impact assessments; require factories to install effluent treatment plants. (2) Implement land-use policies designating forest corridors, with strict penalties for illegal forest clearing.

Environmental Conservation: FUGs regulate timber harvesting, prevent encroachment, and replant degraded areas. Once-degraded hillsides in many mid-hill regions have become thriving forests, increasing wildlife habitat, reducing landslide risk, and allowing deer, leopards, and birds to recover.

Local Livelihoods: Community forests provide firewood, timber, fodder, mushrooms, medicinal herbs, and bamboo. Revenue from controlled timber sales and eco-tourism is reinvested into local schools, irrigation canals, and drinking water systems. Women's active participation in FUG management has improved gender equity in resource decision-making.

a) Gravitational Force: The mutual force of attraction between any two objects having mass; always attractive; F = Gm₁m₂/d².

b) Universal Gravitational Constant (G): The gravitational force between two 1 kg masses placed 1 m apart; G = 6.67 × 10⁻¹¹ Nm²/kg²; constant throughout the universe.

c) Gravity: The special case of gravitational force where one body is a celestial body; F = GMm/R².

d) Acceleration due to Gravity (g): The uniform acceleration produced on a freely falling body by a planet's gravitational pull; g = GM/R²; average on Earth = 9.8 m/s².

e) Weight: The force of gravity acting on an object by a celestial body; W = mg; in Newtons; varies with location.

f) Weightlessness: The condition where a body experiences no normal reaction force, causing it to feel as if it has no weight (e.g., during free fall or in an orbiting satellite).

g) Free Fall: Motion of a body falling solely under gravity with no external resistance; acceleration equals g exactly.

1.96 N — by Newton's Third Law, every action has an equal and opposite reaction; gravitational attraction is mutual.

G = 6.67 × 10⁻¹¹ Nm²/kg²; first measured by Henry Cavendish in 1798 using a Torsion balance.

From F = GMm/R²: gravity depends on (1) Mass of the celestial body (M) — directly proportional; (2) Radius (R) — inversely proportional to R².

g at the poles = 9.83 m/s² (higher than equatorial 9.78 m/s² because the polar radius is smaller).

When upward air resistance equals the downward weight — net force = 0, so acceleration = 0 (terminal velocity).

In a vacuum, a coin and feather fall at the same rate simultaneously, proving g is independent of the mass of the falling body.

When m₁ = m₂ = 1 kg and distance d = 1 m. From F = Gm₁m₂/d² = G × 1 × 1 / 1² = G.

Orbital Motion: Gravity keeps planets revolving in fixed orbits around the Sun — without it, planets would fly off in straight lines.

Ocean Tides: The Moon's gravitational pull creates high tides on Earth's near side and a corresponding bulge on the far side, causing regular tidal cycles.

From Newton's Law of Gravitation: F = GMm/R². From Newton's Second Law: F = mg.

Equating: mg = GMm/R². Dividing both sides by m: g = GM/R².

The mass of the falling body (m) cancels completely — g depends only on M and R of the planet, NOT on the falling object's mass.

(a) Objects fall faster at A (pole) — the polar radius is smaller, giving higher g (9.83 m/s² vs 9.78 m/s² at equator).

(b) Weight decreases from A to B — the larger equatorial radius reduces g = GM/R², and since W = mg (mass constant), weight decreases with g.

(a) g = 25 m/s² means every freely falling object near P gains 25 m/s of speed per second — about 2.55 times stronger gravity than Earth.

(b) Force = 100 × 9.8 = 980 N. On R: m = 980 ÷ 1.62 ≈ 604.9 kg.

His weight in the ISS is effectively zero — weightlessness. The ISS is in continuous free fall around Earth; both the astronaut and station fall at the same rate under gravity, so no normal reaction force acts on him.

a) Newton's law of gravitation is a universal law.

It applies to ALL objects everywhere in the universe with the same G and formula, governing both terrestrial and celestial phenomena without exception.

b) Tides occur in oceans.

The Moon's gravitational pull is stronger on Earth's near side, creating a high tide water bulge; a corresponding bulge forms on the far side due to inertia. Earth's rotation causes two high and two low tides daily.

c) Weight of a body is more in Chitwan than in Solukhumbu.

Solukhumbu is at much higher altitude, increasing distance from Earth's centre — g = GM/(R+h)² decreases, and since W = mg, weight is less at higher altitude.

d) It is difficult to lift a large stone compared to a small one.

A large stone has greater mass, so gravitational force (W = mg) on it is greater, requiring more muscular force to overcome.

e) Earth's mass is ~81× Moon's mass but g_Earth is only ~6× g_Moon.

g = GM/R². Earth's radius is 4× Moon's radius. g_E/g_M = 81/(4²) = 81/16 ≈ 5 ≈ 6. Earth's large radius (squared) counteracts much of its mass advantage.

f) A parachutist can land safely on Earth.

The opened parachute creates large upward air resistance. When air resistance equals weight, net force = 0, acceleration = 0 — parachutist descends at safe constant terminal velocity.

g) Acceleration is produced on a freely falling body.

Gravity exerts a continuous downward force throughout the fall; by Newton's Second Law (F=ma), this constant unbalanced force produces constant acceleration g downward.

h) A parachutist cannot land safely on the Moon.

The Moon has no atmosphere — no air molecules, no drag. A parachute requires air to create resistance; without it, the parachutist accelerates under g_Moon all the way to impact.

i) A flat sheet falls slower than the same paper crumpled into a ball.

The flat sheet has a much larger surface area, creating greater air resistance (drag). In vacuum, both would fall identically.

j) More meteors reach the Moon's surface than Earth's.

Earth's dense atmosphere burns up most meteors by friction ('shooting stars'). The Moon has no atmosphere, so meteors face no resistance and strike directly.

k) Objects become weightless during free fall.

During free fall, both the body and any supporting surface accelerate equally downward — the surface exerts no normal reaction force. Without this push-back, the body feels weightless, though gravity still acts.

Statement: Every body in the universe attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

Proof: Let masses m₁ and m₂ be separated by distance d.

(i) F ∝ m₁ × m₂ (direct proportion to product of masses)

(ii) F ∝ 1/d² (inverse proportion to square of distance)

Combining: F ∝ m₁m₂/d². Introducing constant G: F = G × m₁m₂/d² where G = 6.67 × 10⁻¹¹ Nm²/kg²

This law is 'universal' — applies to all objects everywhere with the same G, governing both terrestrial and celestial bodies.

(i) Distance halved (d → d/2):

F₂ = Gm₁m₂/(d/2)² = 4 × Gm₁m₂/d² = 4F₁

∴ Force INCREASES 4 times when distance is halved.

(ii) Both masses doubled (m₁ → 2m₁, m₂ → 2m₂):

F₃ = G(2m₁)(2m₂)/d² = 4 × Gm₁m₂/d² = 4F₁

∴ Force INCREASES 4 times when both masses are doubled.

All objects fall downward toward Earth's centre with acceleration g ≈ 9.8 m/s².

Objects acquire weight (W = mg); weight varies with g at different locations.

The atmosphere is held around Earth and does not escape to outer space.

Water flows downhill, forming rivers, waterfalls, and streams.

Precipitation (rain, snow, hail) falls from clouds to the ground.

Artificial satellites orbit Earth continuously — gravity provides the centripetal force.

Weightlessness: the condition where a body feels as if it has no weight (normal reaction = 0).

During Free Fall: Both body and supporting surface accelerate equally downward — no normal reaction. Gravity still acts (apparent weightlessness). Example: astronaut in orbiting ISS.

At Earth's Centre: Gravitational pulls from all surrounding mass cancel equally — net g = 0, true weightlessness.

In Deep Space: Far beyond all celestial bodies, gravity is negligibly small — true weightlessness.

Mass is the quantity of matter — depends only on the number and type of molecules; constant everywhere.

Weight = mg. Mass (m) is constant but g varies:

Sea level: g ≈ 9.8 m/s² — standard reference weight.

Top of Mt. Everest: greater distance from Earth's centre → g = GM/(R+h)² decreases → weight less than sea level.

Inside a coal mine: only Earth's mass below the person contributes → effective mass decreases → g decreases → weight less than surface.

Maximum g and weight occur at Earth's surface; they decrease both upward (altitude) and downward (depth).

d = 10 + 16 = 26 m

F = Gm₁m₂/d² = (6.67×10⁻¹¹ × 200 × 400) / 26² = 5.336×10⁻⁶ / 676

Answer: F ≈ 3.16 × 10⁻⁸ N

g = GM/R² = (6.67×10⁻¹¹ × 6×10²⁴) / (6.4×10⁶)² ≈ 9.72 m/s²

m = W/g = 977 / 9.72 ≈ 100 kg

Answer: Mass = 100 kg

g' = GM/(R+h)² = (6.67×10⁻¹¹ × 6×10²⁴) / (6.8×10⁶)²

Answer: g' ≈ 8.61 m/s²

V = (4/3)πR³ = 2.057×10¹⁹ m³ ; M = ρV = 6.99×10²² kg

g = GM/R² = (6.67×10⁻¹¹ × 6.99×10²²) / (1.7×10⁶)²

Answer: g ≈ 1.62 m/s²

M = gR²/G = (9.83 × (6.356×10⁶)²) / 6.67×10⁻¹¹

Answer: M ≈ 5.95 × 10²⁴ kg

g_E = G(10M_J)/(2R_J)² = 2.5 × g_J → g_J = 10/2.5 = 4 m/s²

W_Jupiter = 1 × 4 = 4 N

Answer: Weight on Jupiter = 4 N

(D−d)/d = √(M_S/M_E) = √(3.33×10⁵) ≈ 577 → D = 578d

d = 1.5×10¹¹ / 578 ≈ 2.59×10⁸ m

Answer: d ≈ 2.59 × 10⁵ km from Earth

d₂ = d₁√2 = 3.0×10⁴ × 1.414

Answer: d₂ ≈ 4.24 × 10⁴ km

(R+h)² = R² × (1000/400) = 2.5R² → R+h = 6400 × 1.581 = 10,118 km

h = 10,118 − 6400 = 3,718 km

Answer: h ≈ 3,718 km above Earth's surface

g_planet = G(M_E/2)/(R_E/2)² = 2g_E = 19.6 m/s²

m = 100/1.62 = 61.73 kg ; W = 61.73 × 19.6 ≈ 1210 N

Answer: Weight ≈ 1210 N

h = ½gt² = ½ × 9.8 × 100

Answer: h = 490 m

(a) h = u²/2g = (39.2)²/19.6 = 78.4 m

(b) t to top = 39.2/9.8 = 4 s → Total time = 8 s

(c) By symmetry: velocity at ground = 39.2 m/s

(a) h = u²/2g = 225/19.6 ≈ 11.48 m

(b) t = u/g = 15/9.8 ≈ 1.53 s

(a) 20 = 4t + 5t² → 5t² + 4t − 20 = 0 → t ≈ 1.64 s

(b) v = u + gt = 4 + 10 × 1.64 ≈ 20.4 m/s

a. Thermal Energy: The sum of kinetic energy of all molecules in a body or system.

b. Temperature: Temperature is the measure of the average kinetic energy of the particles in a body.

c. One Calorie: The amount of heat required to raise the temperature of 1 gram of pure water by 1°C.

d. Anomalous Expansion of Water: The property of water in which it contracts (instead of expanding) when heated from 0°C to 4°C.

e. Specific Heat Capacity: The amount of heat required to raise the temperature of 1 kg of a substance by 1°C; SI unit: J/kg°C.

f. Sea Breeze: Sea breeze is the flow of cool air from the sea toward the land during daytime.

g. Digital Thermometer: An electronic device that uses a thermistor (heat-sensitive sensor) to measure and display temperature digitally.

h. Calibration: The process of marking fixed temperature points (upper and lower) on a thermometer to ensure accurate readings.

Bodies with higher temperature feel hotter — heat flows from them into our hand, giving a sensation of warmth.

Heat flows from the hotter body (higher temperature) to the colder body (lower temperature).

1 calorie = 4.2 Joules.

A calorimeter measures the amount of heat absorbed or released during a physical or chemical process.

Heating increases molecular kinetic energy, causing faster vibration that weakens intermolecular forces and increases intermolecular spacing.

Heat gained by the colder body equals the heat lost by the hotter body (when no heat is lost to surroundings).

It works on thermal expansion of liquids — liquid expands and rises in the capillary when heated; contracts and falls when cooled.

It can only measure surface temperature, not internal temperature, and may give incorrect readings on reflective surfaces.

Two bodies have the same temperature but different thermal energy when they differ in mass or substance. Thermal energy depends on mass and nature; temperature depends only on average KE. Example: 1 litre and 2 litres of water both at 100°C — same temperature, but the 2-litre sample has double the thermal energy.

She should dip the metal cap in hot water. The cap expands (increased intermolecular spacing) more than the glass bottle, because metals have a higher coefficient of thermal expansion than glass. This makes the cap slightly larger and easier to remove.

a) The graph shows water's volume decreases (density increases) from 0°C to 4°C, then increases above 4°C — anomalous expansion.

b) Due to anomalous expansion, ice is less dense than water and floats — this is why icebergs float in the ocean.

c) Most substances contract when cooled. Water behaves anomalously between 0°C and 4°C: it contracts when heated and expands when cooled — opposite of normal behaviour.

a) The Arabian Sea surrounds Mumbai. Water's very high specific heat capacity (4200 J/kg°C) means it absorbs/releases heat slowly, moderating temperature to a small 9°C range. Kathmandu is surrounded by land (lower specific heat), which heats and cools quickly, giving a larger 27°C range.

b) If replaced by desert: Mumbai's range would increase dramatically — sand (low specific heat 800 J/kg°C) heats and cools extremely quickly, removing the moderating influence of water.

Heat flows from the hotter to the colder body. The hot body loses thermal energy and temperature; the cold body gains thermal energy and temperature. This continues until both reach the same temperature (thermal equilibrium), after which no further net heat flows.

Alcohol is most likely used. Its freezing point (−114°C) is far below −5°C, ensuring it remains liquid in the freezer. Although mercury (freezing point −39°C) is also liquid at −5°C, alcohol is preferred for sub-zero measurements as it remains liquid at much lower temperatures.

Oil does not expand uniformly with temperature — non-linear expansion makes readings inaccurate.

Oil is adhesive and sticks to glass capillary walls, preventing smooth free movement and causing incorrect readings.

Measures temperature of hot, distant, or moving objects without physical contact.

Provides instant readings and prevents spreading of infections when measuring body temperature.

Uniform (linear) rate of thermal expansion for consistent and accurate readings throughout its temperature range.

Non-adhesive (non-wetting) — should not stick to glass tube walls, allowing free movement for precise readings.

a. Heat and Temperature:

b. Thermal Energy and Temperature:

c. Upper and Lower Fixed Points:

d. Digital and Liquid-in-Glass Thermometer:

a. Water in an earthen pot stays colder than in a metallic vessel.

An earthen pot is porous; water seeps out and evaporates, absorbing latent heat and cooling the remaining water. A metallic vessel is non-porous — no evaporation occurs.

b. Water is used to cool hot vehicle engines.

Water's very high specific heat capacity (4200 J/kg°C) allows it to absorb large amounts of engine heat with only a small temperature rise — an excellent coolant.

c. Wet cloth is placed on a fever patient's forehead.

The wet cloth absorbs large amounts of heat (high specific heat capacity of water); additionally, evaporation absorbs latent heat of vaporisation from the forehead, further cooling it.

d. Desert days are hot and nights are very cold.

Sand has low specific heat capacity (800 J/kg°C), heating quickly in sun and cooling rapidly at night. No large water body moderates the temperature.

e. A thick glass tumbler may crack when hot water is poured in.

Glass is a poor heat conductor; the inner surface expands rapidly while the outer surface remains cool. This differential expansion creates internal stress that cracks the glass.

f. Some space is left empty in sealed cold drink bottles.

The empty space accommodates thermal expansion of the liquid when temperature rises, preventing dangerous pressure buildup inside the sealed bottle.

g. Overhead electricity cables sag between poles in summer.

High summer temperatures cause metal wires to expand and lengthen; since pole distance is fixed, the extra wire length causes sagging between poles.

h. Gaps are left between rails while constructing railway tracks.

Metal rails expand in summer; without gaps, expanding rails would push against each other, building compressive forces that could cause them to buckle dangerously.

Due to anomalous expansion, water contracts from 0°C to 4°C — volume decreases while mass stays constant, so density = mass/volume increases. Above 4°C, water expands normally (density decreases). Hence maximum density at 4°C.

j. Aquatic animals survive in ponds frozen during winter.

Water at 4°C (maximum density) sinks to the bottom; layers form: 4°C at bottom, 0°C at surface. Surface water freezes forming an insulating ice layer; fish survive in the liquid water below.

k. Taps are left open during winter nights in the Himalayan region.

Below 0°C, frozen water expands due to anomalous expansion, creating pressure that can burst pipes. Leaving taps open keeps water flowing, preventing freezing and relieving pressure.

l. Mountaineers carry alcohol thermometers instead of mercury thermometers.

Mercury freezes at −39°C, making it useless in extreme mountain cold. Alcohol (freezing point −114°C) remains liquid at the lowest temperatures encountered on mountains.

m. Upper and lower fixed points are determined under standard atmospheric pressure.

The boiling and freezing points of water change with pressure; standard atmospheric pressure (760 mmHg) ensures all thermometers worldwide are calibrated consistently.

Thermal Energy is the total KE of all molecules in a body — depends on mass, temperature, and nature of substance. A large tank of lukewarm water has more thermal energy than a small cup of hot tea despite lower temperature, because it contains more molecules.

Temperature measures average KE of molecules — does NOT depend on mass or quantity.

Heat is thermal energy in transit — flows from hotter to colder body due to temperature difference; it is NOT stored.

Example: Hot metal ball placed in cold water — heat flows from ball to water. Ball's temperature and thermal energy decrease; water's increase — until thermal equilibrium is reached.

Air expands the most, followed by water, then glass.

Solids (Glass): Tightly packed molecules with strong forces — expansion is minimum.

Liquids (Water): Larger intermolecular spaces and weaker forces than solids — expansion is moderate.

Gases (Air): Very large spaces with very weak forces; molecules spread out with almost no restriction — expansion is maximum.

Order: Air > Water > Glass.

Let a body of mass m rise in temperature from t₁ to t₂ when heat Q is supplied. Change in temperature dt = t₂ − t₁.

From experiments: (i) Q ∝ m (ii) Q ∝ dt

Combining: Q ∝ m × dt. Introducing proportionality constant S: Q = mSdt

Where S = specific heat capacity of the substance.

a) X has the most thermal energy — with equal mass and same temperature, Q = mSdt, so highest S means most heat stored.

b) X penetrates deepest into wax — stores most thermal energy; releases most heat to melt wax and sinks deepest.

c) Z shows greatest temperature change — from dt = Q/mS, with equal Q and m, lowest S gives greatest dt.

d) S of Y = 380 J/kg°C means 380 Joules are required to raise the temperature of 1 kg of Y by 1°C.

Advantages:

Ice floats on water (less dense when frozen), protecting aquatic ecosystems from freezing solid.

Aquatic organisms survive winter: water at 4°C sinks to the bottom; ice layer at the surface insulates the water below.

Stable aquatic environments maintained even in harsh winters.

Disadvantages:

Water pipes crack in winter when frozen water expands and builds up pressure.

Water in cracks of rocks and roads expands on freezing, widening cracks and causing structural damage.

Sealed containers fully filled with water may break when the contents freeze.

A. Liquid-in-Glass: Works by thermal expansion of liquid — liquid expands and rises in the capillary when temperature increases; contracts and falls when it decreases. Height of column indicates temperature.

B. Digital Thermometer: Uses a thermistor sensor that converts temperature change into an electrical signal, processed by a microprocessor and displayed as a digital reading.

C. Radiation (Infrared) Thermometer: Detects infrared radiation emitted by a body's surface; a thermopile converts it into an electrical signal and displays temperature digitally — no physical contact required.

Step 1 — Lower Fixed Point (0°C / Ice Point): Place bulb in crushed ice-water mixture at standard atmospheric pressure; when alcohol column stabilises, mark this level as 0°C.

Step 2 — Upper Fixed Point (100°C / Steam Point): Hold bulb in steam above boiling pure water at standard atmospheric pressure; when column stabilises, mark this level as 100°C.

Step 3 — Divide Scale: Measure distance between 0°C and 100°C marks; divide into 100 equal parts (each = 1°C). Thermometer is now calibrated.

From S = Q/(m×dt), with equal Q and m: S ∝ 1/dt. Y had smaller temperature change (5°C), so Y has HIGHER specific heat capacity.

Y is better for heating and cooling: (1) High S — absorbs large heat for small temperature rise, excellent coolant (e.g., engine radiators). (2) Stores and releases heat slowly — excellent for heating applications (e.g., hot water bags).

Q = mSdt = 7 × 460 × 10

Answer: Q = 32,200 J

dt = Q/(mS) = 1,008,000 / (20 × 4200)

Answer: dt = 12°C

S = Q/(m×dt) = 19,000 / (5 × 10)

Answer: S = 380 J/kg°C

Water minimum volume at 4°C. dt = 24 − 4 = 20°C ; m = 2000 g

Q = 2000 × 1 × 20

Answer: Q = 40,000 Calories

Heat lost = Heat gained: 5(80−t) = 1(t−20)

400 − 5t = t − 20 → 420 = 6t

Answer: t = 70°C

60S(100−40) = mS(40−15) → 60×60 = m×25

Answer: m = 144 kg

Q = 2 × 470 × 117 = 109,980 J

dt_silver = 109,980 / (2 × 234) = 235°C

Answer: Final temperature of silver = 20 + 235 = 255°C

a. Refraction of Light: The bending of light as it passes from one medium to another due to a change in speed.

b. Refractive Index: The ratio of speed of light in vacuum (c) to its speed in a medium (v); μ = c/v.

c. Critical Angle: The angle of incidence in the denser medium at which the refracted ray just grazes the surface (angle of refraction = 90°).

d. Mirage: An optical illusion of water on hot roads or deserts caused by total internal reflection of light in hot air layers near the ground.

e. Optical Fiber: A thin flexible strand of glass or plastic that transmits light signals over long distances using total internal reflection.

f. Concave Lens: A lens that is thin at the middle and thick at edges; causes parallel rays to diverge (diverging lens).

g. Focal Length: The distance between the principal focus and optical centre of a lens (positive for convex, negative for concave).

h. Power of Lens: The converging or diverging ability of a lens; P = 1/f (in metres); SI unit: diopter (D).

j. Colour Blindness: A condition where a person cannot distinguish certain colours due to defects in cone cells of the retina.

k. Hypermetropia: Vision defect where near objects appear blurred but distant objects are clear; image of near objects forms behind the retina.

l. Cataract: A condition where the eye lens becomes cloudy due to protein breakdown, causing blurry or dim vision.

The change in speed of light when it passes from one medium to another — the greater the speed difference, the greater the bending.

Medium B is denser; Medium A is rarer — light bends away from normal when moving from denser to rarer medium.

A right-angled isosceles prism (90°–45°–45°) — light strikes its hypotenuse at 45°, exceeding the critical angle of glass (~43°), causing total internal reflection.

Optical fibres in an endoscope use total internal reflection to carry light into the body and transmit images of internal organs to the doctor.

Place a second identical prism in an inverted position after the first — it reverses the dispersion and recombines all seven colours back into white light.

If m > 1, the image is magnified — it is larger than the actual object.

Keyhole surgery uses very small cuts, causing less pain, smaller scars, lower infection risk, and much shorter recovery than traditional open surgery.

Ciliary muscles relax, causing the lens to become thin and flat with a longer focal length, focusing the distant image exactly on the retina.

This is myopia (short-sightedness) — the person can see nearby objects clearly but not distant ones.

Defect B (insufficient ciliary contraction + shortened eyeball) is hypermetropia (long-sightedness) — corrected by a convex lens.

Rhodopsin is mainly made from Vitamin A — a light-sensitive pigment in rod cells essential for dim-light vision.

Contact lenses sit directly on the eye, providing a wider field of vision than spectacles.

Never rub eyes when dust enters — gently rinse with clean water to flush out foreign particles without scratching the cornea.

The donated cornea is preserved in a special solution in an eye bank (e.g., Tilganga Institute, Nepal) and must be transplanted within two weeks of removal.

First Law: The incident ray, refracted ray, and the normal at the point of incidence all lie in the same plane.

Second Law (Snell's Law): The ratio of sine of angle of incidence to sine of angle of refraction is a constant (μ = sin i / sin r) for the same two media. This constant is called the refractive index.

It means light travels 1.5 times slower in glass than in vacuum. When light passes from air into glass, it bends toward the normal because it slows down. The higher the refractive index, the denser the medium and the more light bends.

Condition 1: Light must travel from an optically denser medium to a rarer medium (e.g., glass to air).

Condition 2: The angle of incidence in the denser medium must be greater than the critical angle (i > C). When both are satisfied, all light reflects back into the denser medium.

An optical fibre works on total internal reflection. Light enters the denser core (higher refractive index). When it strikes the core-cladding boundary at an angle > critical angle, it is completely reflected back. Through repeated total internal reflections along the entire length, light travels with minimal energy loss — even around bends.

A ray enters perpendicular to one face (no bending at entry). It strikes the hypotenuse at 45° (> critical angle of glass ~43°), so total internal reflection occurs. The ray then exits perpendicular to the adjacent face. The incident ray is deviated by 90°. Application: periscopes.

Properties of the image:

Position: Beyond 2F on the other side of the lens

Size: Magnified (larger than the object)

Nature: Real and Inverted

Application: Slide projectors.

A convex lens is like a combination of prisms with thicker edges at the centre. Upper half: rays refract downward toward the axis. Lower half: rays refract upward. The combined effect converges all parallel rays to a single principal focus — hence it is a converging lens.

Place the light source exactly at the principal focus (F) of the convex lens. All diverging rays from the source are refracted and emerge as a parallel beam. Application: search lights, torches, and car headlights.

The eye lens has power of accommodation — it changes focal length through ciliary muscles. For distant objects: muscles relax → lens becomes thin → focal length increases → image on retina. For near objects: muscles contract → lens becomes thick → focal length decreases → image on retina.

f = 1/P = 1/(−2.5) = −0.4 m = −40 cm

Answer: Focal length = −40 cm. Negative sign confirms this is a concave lens.

Dr. Ruit's Small-Incision Cataract Surgery (SICS) removes cataracts through a small cut without stitches, using affordable intraocular lenses produced in Nepal. It offers reduced surgery time, fewer complications, shorter recovery, and low cost — making cataract surgery accessible to rural and remote communities, restoring sight to hundreds of thousands who would otherwise remain blind.

Wash and dry hands thoroughly before handling lenses.

Clean lenses daily with the recommended cleaning solution.

Never sleep with contact lenses on.

Never share contact lenses with others.

Remove lenses before swimming or showering.

a) Problem A is Hypermetropia (long-sightedness) — the chart shows correction by increasing corneal curvature (adding converging power) through laser surgery.

b) Problem B is Myopia (short-sightedness). Another method besides laser surgery: wearing spectacles with a concave lens of suitable focal length.

a. Ray of light bends when passing from one medium to another.

When light passes from one medium to another, its speed changes — one part of the wavefront slows before the rest, causing a change in direction (bending). Greater speed difference = greater bending.

b. A coin inside a glass appears to rise when water is poured in.

Light from the coin travels from water (denser) to air (rarer) and bends away from normal. Refracted rays appear to come from a shallower virtual position — the coin appears raised.

c. A fisherman cannot hit a fish by striking at its apparent position.

The fish appears at a shallower position than its actual depth due to refraction. Aiming at the apparent position causes the spear to miss the actual fish, which is deeper in the water.

d. A pencil immersed in water appears bent.

Light from the submerged portion refracts at the water-air surface (bends away from normal), making it appear displaced. Light from the above-water portion is unaffected — the mismatch creates the appearance of bending.

e. Stars twinkle but planets do not.

Stars are point sources; their light fluctuates through varying atmospheric layers, causing twinkling. Planets appear as small discs; random refractions from different parts of the disc average out — planets appear steady.

f. The Sun is seen ~2 minutes before actual sunrise and ~2 minutes after actual sunset.

Earth's atmosphere has increasing density toward the ground. Sunlight refracts continuously along a curved path, allowing us to see the Sun when it is still slightly below the horizon.

g. Sound travels farther at night than during the day.

At night, cooler denser air near the ground refracts sound waves downward, keeping them close to Earth and allowing them to travel farther. During the day, warm near-surface air refracts sound upward.

h. A prism is used in a periscope instead of mirrors.

A right-angled isosceles prism reflects 100% of light by total internal reflection — no energy loss. Ordinary mirrors absorb some light and can tarnish; prisms produce brighter, clearer images and are more durable.

Hot road surfaces create layers of hot rarer air near the ground with denser cooler air above. Sunlight refracts continuously through these layers; when the angle of incidence exceeds the critical angle, total internal reflection occurs, creating the illusion of water or sky reflections on the road.

j. A diamond sparkles but a glass slab of similar shape does not.

Diamond has a very high refractive index (2.42) and tiny critical angle (24°). Light easily exceeds this angle internally, causing total internal reflection at almost every surface. Glass (critical angle 43°) allows light to escape more easily — hence no sparkling.

k. Optical fibres can transmit signals at very high speeds.

Optical fibres carry data as light signals travelling at ~3×10⁸ m/s with very high frequency. Total internal reflection ensures almost zero energy loss over long distances — far superior to copper wires.

l. Doctors can observe internal organs using an endoscope.

An endoscope uses bundles of optical fibres. One bundle carries light in to illuminate organs; another transmits reflected images back out via total internal reflection. Clear bright images are obtained without invasive surgery.

m. Constituent colours of white light are separated when passing through a glass prism.

White light contains seven colours (VIBGYOR) each with different wavelengths and speeds in glass. Violet (shortest wavelength) bends most; red (longest) bends least. Refraction at both prism surfaces separates them into a visible spectrum.

n. A concave lens is called a diverging lens.

A concave lens is thin at the middle and thick at edges — it acts like prisms with thin edges at the centre. All regions refract rays outward, causing them to spread apart (diverge) after passing through.

o. A convex lens corrects long-sightedness (hypermetropia).

In hypermetropia, near objects form an image behind the retina. A convex lens pre-converges light from nearby objects before it enters the eye, bringing the focal point forward exactly onto the retina.

p. Power of a concave lens is negative.

The focal length of a concave lens is negative (virtual focus on the same side as incoming light). Since Power = 1/f, and f is negative, power is also negative.

q. We cannot see properly when entering a dark room from bright light.

In bright light, the iris contracts the pupil. In a dim room, the pupil must dilate to let more light in — this iris adjustment takes several seconds to a minute. During this adjustment, insufficient light reaches the retina.

r. People with night blindness cannot see well in low light.

Rod cells contain rhodopsin (made from Vitamin A) for dim-light vision. In night blindness, rod cells malfunction or rhodopsin is lacking (usually Vitamin A deficiency), preventing effective dim-light detection.

a. Optically Denser and Rarer Medium:

b. Angle of Incidence and Critical Angle:

c. Concave Lens and Convex Lens:

d. Myopia and Hypermetropia:

e. Cornea and Eye Lens:

f. Colour Blindness and Night Blindness:

g. Spectacles and Contact Lenses:

μ = sin i / sin r → 1.5 = sin 30° / sin r → sin r = 0.5/1.5 = 0.333

Answer: r = sin⁻¹(0.333) ≈ 19.5°

v = c/μ = (3×10⁸) / 1.33

Answer: v ≈ 2.26 × 10⁸ m/s

1/v − 1/u = 1/f → 1/v = 1/10 + 1/(−20) = 1/20 → v = 20 cm

m = v/u = 20/(−20) = −1

Answer: Image distance = 20 cm (real, on other side). Magnification = −1 (same size, real, inverted).

sin C = 1/μ = 1/1.5 = 0.6667 → C = sin⁻¹(0.6667) ≈ 42°

Critical angle ≈ 42°

TIR for ray from air onto glass? NO — TIR requires light to travel from DENSER to RARER medium.

Air (μ=1.0) is rarer than glass (μ=1.5); a ray going from air → glass is rarer-to-denser, so TIR is impossible.

100°C / 212°F / 373 K | 0°C / 32°F / 273 K

∠ABM (i) | Angle of Incidence

∠CBN (r) | Angle of Refraction