Chapter 4 — Light and everyday optical phenomena

Begin with a ray, then choose the boundary

Light can travel through a vacuum and, in a uniform transparent medium, is often represented by straight rays. A ray is a drawing device: it records a direction of energy travel and helps predict where an image forms. A narrow beam entering water from air is one kind of boundary problem; a beam bouncing from a polished surface is another. Read the stem for the medium on each side and for whether the light continues through the boundary or returns into its original medium. That distinction selects refraction or reflection before any formula is needed.

The normal is an imaginary line perpendicular to the surface at the point where a ray meets it. Angles of incidence, reflection and refraction are measured from this normal, not from the surface itself. If an incident ray is said to make 30° with a plane mirror's surface, it makes 60° with the normal. The angle of reflection is then 60° relative to the normal. A common distractor answers 30° after measuring from the wrong line. Draw the normal first even when the MCQ supplies a picture.

Reflection and image location

For a smooth reflecting surface, the angle of reflection equals the angle of incidence, and the incident ray, reflected ray and normal lie in one plane. These statements apply to each individual ray. A rough wall reflects light too, but its tiny surface orientations vary, producing diffuse reflection. The wall therefore looks visible from many directions without behaving like a neat face mirror. “Diffuse reflection” does not mean the law of reflection stops working; it means the local normals differ across the surface.

A plane mirror produces an upright, virtual image that appears as far behind the mirror as the object is in front, under the idealised geometry. The image cannot be caught on a screen behind the mirror because light does not actually converge there. The familiar left–right reversal needs careful language: the mirror reverses front and back relative to its plane; our left–right impression arises when we compare ourselves with a person imagined to have turned around. For an exam item, the reliable facts are virtual, erect, same size and equal object/image distances from the mirror.

If a person approaches a stationary plane mirror by 1 m, the image also approaches the mirror by 1 m from the apparent side. The separation between person and image decreases by 2 m. This is a two-distance calculation: the person–mirror gap and mirror–image gap both change. A different question could ask only how far the image shifts, which is 1 m. State the requested endpoints before choosing between those answers.

Curved mirrors and where images can form

A concave mirror curves inward on its reflecting side and can converge rays parallel to the principal axis toward a focus in the paraxial approximation. A convex mirror curves outward and spreads reflected rays; its image is virtual, upright and diminished for a real object in standard school-level treatment. This wide field of view is why convex mirrors are useful as rear-view or surveillance mirrors. A concave mirror may produce a magnified upright image when an object is within its focal distance, but its image changes character when the object is farther away. Do not claim that every concave-mirror image is magnified or real without the object position.

The centre of curvature of a spherical mirror is the centre of the sphere from which the surface could be imagined to be cut. The radius of curvature R is the distance from mirror pole to that centre; focal length is R/2 in the paraxial spherical-mirror model. A focus is not the same as the centre of curvature. For a multiple-choice diagram, locate the pole, focus and centre in the correct order before extending rays. Sign conventions can differ among books; use the convention stated by the problem when substituting into mirror formulas.

Refraction is a change in propagation direction

Light can bend at a boundary when its speed changes from one medium to another. At normal incidence it can change speed without bending, so “refraction always bends the ray” is too broad. For oblique entry from air into ordinary glass, the transmitted ray bends toward the normal; from glass back to air it bends away. The frequency remains the same across a stationary boundary, while speed and wavelength change. If a question asks which property does not change on crossing, frequency is the usual answer in this model.

A straw partly immersed in water appears displaced at the surface because rays from its submerged part refract before reaching the eye. The object did not physically bend. A swimming pool can appear shallower than its true depth when viewed obliquely from air due to the paths of light from the bottom. This visual shift is an observation about ray paths; do not treat an apparent depth as a directly measured geometric depth. Label the actual object, refracted ray and backward extension used to locate the apparent image.

Refractive index compares light speed in vacuum with light speed in a medium: n = c/v for a simple transparent medium at a stated wavelength. A larger n means lower light speed there compared with vacuum. It does not mean that frequency drops at the boundary. For air-to-glass questions, the exact value depends on the glass and wavelength, so use a value supplied in the stem. In a glass slab with parallel faces, the emergent ray can be parallel to the incident ray but laterally displaced. A prism has nonparallel faces and can produce a net deviation and, for white light, dispersion of colours because refractive index varies with wavelength.

Lenses and a controlled ray diagram

A convex lens is thicker at the centre than at the edges and can converge paraxial rays from a distant object toward a focus. A concave lens is thinner at the centre and spreads incoming paraxial rays. The image made by a concave lens for a real object is virtual, upright and smaller in the standard simple-lens model. A convex lens can form a real inverted image on a screen for some object positions, or a virtual upright magnified image when the object is within the focal length. Object position is therefore indispensable for convex-lens image questions.

Use two well-defined rays to construct a simple image. A ray through the optical centre of an ideal thin lens is drawn approximately undeviated. A ray parallel to the principal axis refracts through the far focus for a convex lens. Where the actual emerging rays meet gives a real image; where their backward extensions meet gives a virtual image. Do not infer that an image is real just because its apparent position is drawn on paper. The criterion is whether the actual outgoing rays converge and can form the image on a screen.

Lens power P is 1/f when focal length f is measured in metres, and its unit is the dioptre (D). A convex converging lens has positive power under the usual school sign convention, while a concave diverging lens has negative power. A lens with focal length +0.5 m has power +2 D. If the focal length is given as +50 cm, convert to 0.5 m before taking the reciprocal. Taking 1/50 and calling it dioptres is a unit error. In corrective lenses, the appropriate lens depends on the visual defect; this book treats the optical principle, not personal vision advice.

Human eye, colour and atmospheric effects

The cornea and lens help focus light onto the retina. The retinal image is real and inverted in the optical sense, while the visual system interprets the scene. The eye's lens changes shape to adjust focus over a range; this is accommodation. A camera-like analogy helps with image formation, but the biological retina and neural processing make the eye more than a simple camera. When an MCQ asks whether the retina's image is real or virtual, follow the optics definition: converging rays actually meet on the retinal surface, so it is real.

White light can be dispersed into a spectrum when different wavelengths are refracted by different amounts. A rainbow involves refraction, internal reflection and dispersion in water droplets; calling it “reflection only” leaves out essential steps. The sky's blue appearance is related to wavelength-dependent scattering of sunlight in Earth's atmosphere, while the red or orange appearance near sunrise and sunset involves a longer atmospheric path and removal of much shorter-wavelength light from the direct beam. The precise colour of a photographed sky also depends on particles, clouds and viewing conditions, so an exam answer should match the stated idealised mechanism rather than overgeneralise from one image.

Test a mirror answer by tracing two rays

For a point object in front of a plane mirror, draw two rays from the point toward two different spots on the mirror. Reflect each so its angle to the local normal equals the incident angle. The reflected rays diverge in front of the mirror; extend them backward with dashed lines. Their backward extensions meet behind the mirror at the virtual image point. This construction explains both the apparent position and the inability to project the image onto a screen placed behind an ordinary opaque mirror. It also explains why the image position moves when the object moves: the equal-distance geometry is reconstructed from the rays at each new object position.

If a mirror rotates while an incident ray remains fixed, the reflected direction changes by twice the mirror rotation angle in the simple plane geometry. One way to see this is that rotating the mirror rotates its normal by the same angle; the incidence angle changes relative to the new normal, and the reflected ray must change by the corresponding amount on the other side. A 5° mirror rotation can therefore deflect the reflected ray by 10° under these conditions. Do not confuse this with moving a mirror bodily without rotating it: a translation can shift the ray's intercept or the apparent image position without the same angular rule. An MCQ must specify the operation before the factor of two is applied.

For a convex mirror, reflected rays diverge and their backward extensions meet behind the mirror. As a real object moves closer in the usual axial model, the virtual image remains behind the mirror and upright; it can grow while remaining diminished relative to the object. A concave mirror has more possibilities. An object beyond its centre of curvature gives a real, inverted, diminished image between centre and focus. At the centre, the ideal image is real, inverted and same-sized. Between centre and focus, it is real, inverted and magnified beyond the centre. Inside the focus, outgoing rays diverge and their backward extensions give a virtual upright magnified image. These positions make a useful ordered diagram; memorising only “concave magnifies” loses three cases.

Refractive index and critical angle

Snell's relation for a simple boundary is n₁sin i=n₂sin r, with both angles measured from the normal. If light passes from air with approximate index 1 into glass of index 1.5 at an incidence angle of 30°, then sin r=(1/1.5)sin 30°=1/3. Thus r is about 19.5°, smaller than 30°, showing a bend toward the normal. In a police exam, the numerical inverse-sine step is less common than choosing the direction of bend; the formula gives a check on that direction. At normal incidence, i=0 and r=0, but the speed still changes between media. The ray does not visibly change direction simply because it entered at zero angle.

Total internal reflection can occur when light travels from a medium of higher refractive index toward one of lower index and its incidence angle exceeds the critical angle. There is no transmitted refracted ray carrying energy away in the ideal simple model; the light is reflected internally. The conditions matter. Light travelling from ordinary air into glass cannot show total internal reflection at that entry boundary because it moves toward the higher-index medium. For a glass-to-air boundary with indices 1.5 and 1, sin c=n₂/n₁=2/3, so the critical angle c is about 41.8°. At a smaller angle there is refraction as well as reflection; at a larger angle the ideal ray is internally reflected. A question offering “any angle at any boundary” is too broad.

Optical fibres guide light using internal reflection in a core surrounded by material of lower effective refractive index, though real fibre operation is described more completely by wave optics and may involve attenuation. A road mirage is also a refraction phenomenon associated with air layers of different temperature and refractive index; calling it simply a mirror reflection from the road is misleading. These examples are useful only after the boundary conditions are understood. The exam's core question is usually which way the ray bends or which condition permits total internal reflection, not how to build a telecommunications system.

Lens cases by object distance

For a convex lens, a distant object sends approximately parallel rays, which meet near the focus on the far side. An object beyond twice the focal length forms a real, inverted, smaller image between one and two focal lengths on the other side. At twice the focal length, the simple ideal image is real, inverted and same-sized at twice the focal length. Between one and two focal lengths, it is real, inverted and larger beyond twice the focal length. At the focal position, the emerging ideal rays are parallel and do not meet at a finite image distance. Inside the focal length, the image is virtual, upright and magnified on the object's side. A magnifying glass works in that final case. The sequence explains why “convex lens always gives a real image” is false.

A concave lens with a real object gives a virtual, upright, reduced image in the standard thin-lens model. It cannot project that image onto a screen. To decide whether an optical image is real, follow the actual outgoing rays rather than judging whether an image appears visible to an observer. A virtual image can be seen by an eye because the entering rays appear to come from its location when traced backward. Visibility does not imply that the image can be recorded on a screen at that apparent point. This distinction unifies plane mirrors, convex mirrors and concave lenses.

The lens equation can be useful if a problem supplies a sign convention. In a simple real-object setup using positive magnitudes for object and real-image distances, 1/f=1/u+1/v for a convex lens. With f=10 cm and u=30 cm, 1/v=1/10−1/30=2/30=1/15, so the real image lies 15 cm on the other side. The magnitude of magnification is v/u=15/30=1/2, consistent with an object beyond 2f producing a smaller image between f and 2f. Other school texts use Cartesian signed distances instead of these positive magnitudes. Do not mix conventions mid-calculation; draw the geometry and follow the one specified in the question.

Corrective optics as a principle

In the basic eye model, myopia means distant objects focus in front of the retina when the eye is uncorrected; a diverging concave lens can shift the effective focus back onto the retina. Hypermetropia means near objects tend to focus behind the retina in the simplified model; a converging convex lens can help bring the focus forward. Age-related presbyopia arises largely because the crystalline lens becomes less flexible and accommodation for near viewing declines. A question about presbyopia's mechanism should not be answered with the cause of astigmatism, which is linked to uneven curvature of optical surfaces. These are exam-level optical descriptions; an individual's prescription requires an eye examination.

A corrective lens marked −2 D has negative power and focal length f=1/P=−0.5 m under the usual convention. Its negative sign identifies a diverging lens; it is not a negative physical length that can be measured with a ruler. A +4 D lens has focal length +0.25 m and is converging. The larger absolute dioptre value has the shorter absolute focal length: a +4 D lens is optically stronger than a +2 D lens under this simple comparison. Convert centimetres to metres before taking the reciprocal, and keep the sign through the answer.

Worked two-part example

A ray meets a plane mirror at 25° to its surface. Because the normal is perpendicular to the surface, the angle of incidence is 90°−25°=65°. The angle of reflection is 65° to the normal, or 25° to the mirror surface on the other side. Now consider an ideal lens with focal length +25 cm. Convert to +0.25 m; power is 1/0.25=+4 D. The first task depends on angle reference; the second depends on length unit. In both, writing the reference line or unit before calculating prevents the most plausible wrong option.

Active recall before the practice set

Sketch a normal at a flat reflecting surface and label both angles from that line. Explain why a rough wall can reflect light without showing a clear image. State the plane-mirror image properties and calculate how person–image separation changes when the person moves closer. Describe what stays unchanged when light enters glass and what can change. Give one possible real-image situation for a convex lens and one virtual-image situation. Convert 50 cm focal length into dioptres. After each answer, ask whether you relied on a diagram, a definition or a calculation; the chapter practice includes all three.

Figure 4. Original chapter diagram.

Practice 36 questions

Choose one answer for each item. The answer key and explanations follow this chapter set.

1. The Sun appears red or orange at sunrise and sunset mainly because:

A. The Sun emits more red light in the evening B. Clouds absorb red light less than other colours C. Sunlight travels a longer path through the atmosphere and most of the blue light is scattered away D. The Sun becomes cooler at the horizon

2. A plane mirror makes your left hand appear as the right hand of your image. This left-right reversal is called:

A. Lateral inversion B. Total internal reflection C. Dispersion D. Accommodation

3. Which type of lens is used in a magnifying glass?

A. Concave lens B. Cylindrical lens C. Bifocal lens D. Convex lens

4. Assertion (A): A bird touching only one high-voltage wire with both feet close together can often sit without a significant electric shock.
Reason (R): The bird's body is a perfect insulator and cannot conduct current.
Select the correct option.

A. Both A and R are true and R is the correct explanation of A B. Both A and R are true but R is not the correct explanation of A C. A is true but R is false D. A is false but R is true

5. Assertion (A): The sky appears blue and not violet.
Reason (R): Sunlight contains less violet light and human eyes are less sensitive to violet, even though violet is scattered more strongly than blue.
Select the correct option.

A. Both A and R are true and R is the correct explanation of A B. Both A and R are true but R is not the correct explanation of A C. A is true but R is false D. A is false but R is true

6. A simple periscope used in submarines consists of two plane mirrors placed parallel to each other at an angle of:

A. 30° B. 60° C. 45° D. 90°

7. Match each phenomenon with its main introductory explanation.
List I: A. Blue sky; B. Rainbow after rain; C. Mirage above a hot road; D. Needle supported at a water surface.
List II: 1. Surface tension; 2. Refraction through layers of air; 3. Scattering of light; 4. Dispersion of light.

A. A-3, B-4, C-2, D-1 B. A-4, B-3, C-2, D-1 C. A-3, B-2, C-4, D-1 D. A-2, B-4, C-3, D-1

8. A force of 50 N acts perpendicularly on an area of 0.01 m². What pressure does it exert?

A. 500 Pa B. 5,000 Pa C. 0.5 Pa D. 50,000 Pa

9. Thunder is heard 6 seconds after a flash of lightning is seen. Taking the speed of sound in air as 340 m/s, roughly how far away is the storm?

A. About 1 km B. About 6 km C. About 20 km D. About 2 km

10. In a primary rainbow, which colour appears on the outer edge of the arc?

A. Violet B. Red C. Green D. Blue

11. The appearance of a "pool of water" on a hot road on a summer afternoon (mirage) is due to:

A. Refraction through air layers with different refractive properties B. Scattering of light by dust particles C. Dispersion of light by water vapour D. Reflection of sunlight from a thin water film on the road

12. A thin convex lens has a focal length of +0.5 m. What is its optical power?

A. −2 dioptres B. +0.5 dioptre C. −0.5 dioptre D. +2 dioptres

13. A bird sitting on a single high-voltage wire does not get an electric shock because:

A. Birds' feet are perfect insulators B. The wire carries direct current C. High-voltage wires carry almost no current D. There is no significant potential difference between its two feet

14. A ceiling fan makes us feel cooler in summer because it:

A. Increases the rate of evaporation of sweat from the skin B. Lowers the temperature of the room air C. Absorbs heat from the room and releases it outside D. Increases the humidity of the room

15. A pressure cooker cooks food faster than an open pan mainly because:

A. Increased pressure raises the boiling point of water above 100°C B. Increased pressure lowers the boiling point of water C. Steam inside the cooker is cooler than boiling water D. The sealed lid stops water from ever boiling

16. It is difficult to cook rice in an open pan at high altitudes such as Ladakh because:

A. Higher atmospheric pressure raises the boiling point of water B. Lower atmospheric pressure lowers the boiling point of water C. Water cannot boil at all at high altitude D. Cold air removes all heat from the pan

17. Polarised sunglasses reduce the glare from a wet road or a water surface because they:

A. Darken all colours of light equally, as ordinary tinted lenses do B. Bend the glare rays away by refraction in a concave lens C. Increase the amount of light entering the eye D. Preferentially pass vertical polarization and suppress much of the horizontally polarized reflected glare

18. With a fixed incident ray, a plane mirror is rotated by 10° about an axis perpendicular to the plane of incidence. Through what angle does the reflected ray turn?

A. 5° B. 10° C. 30° D. 20°

19. Camels walk easily on soft desert sand without sinking much because their broad, flat feet:

A. Spread the body weight over a larger area and so reduce the pressure on the sand B. Increase the friction between the feet and the sand C. Reduce the total weight of the camel D. Increase the pressure so that the feet grip the sand firmly

20. In a conventional AC power-transmission system, why is the voltage stepped up for a long transmission line and then stepped down near users?

A. AC is inherently safer to touch than DC B. AC travels along wires faster than DC C. DC cannot flow through overhead aluminium wires D. Transformers can change AC voltage efficiently; a higher line voltage permits lower current and lower I²R loss for a given power

21. Which type of mirror does a dentist use to get an enlarged, upright view of a tooth?

A. Concave mirror B. Convex mirror C. Plane mirror D. Cylindrical mirror

22. Consider the following statements:
Statement I: A steel ship floats because its hollow shape displaces a large volume of water whose weight equals the ship's weight.
Statement II: A steel needle placed gently flat on water floats mainly because of Archimedes' principle.
Which of the above statements is/are correct?

A. Only I B. Only II C. Both I and II D. Neither I nor II

23. Which of the following is NOT an example of cooling by evaporation?

A. Water cooling in an earthen matka B. Sweating cooling the human body C. A thermos flask keeping tea hot D. Refrigerant cooling the inside of a refrigerator

24. Arrange the following events in the correct order in which they happen to sunlight inside a raindrop to form a rainbow:
A. Internal reflection at the back of the drop
B. Refraction as light leaves the drop
C. Refraction (with dispersion) as light enters the drop

A. C, A, B B. A, C, B C. C, B, A D. B, A, C

25. A compound microscope consists of:

A. Two concave lenses B. Two convex lenses — an objective and an eyepiece C. One convex lens and one concave lens D. A concave mirror and a plane mirror

26. A light ray enters glass from air exactly along the normal to a flat surface. Which statement is correct?

A. Its speed changes in glass, but its direction does not bend at the boundary B. It bends away from the normal C. It bends toward the normal through a visible angle D. It is totally internally reflected back into the air

27. Large astronomical telescopes generally use which component to gather faint starlight?

A. A large convex mirror B. A large concave lens C. A large concave mirror D. A plane mirror

28. Optical fibres used in high-speed internet cables work on the principle of:

A. Dispersion B. Total internal reflection C. Diffraction D. Scattering

29. A boy stands 2 m in front of a plane mirror and then walks 0.5 m towards it. What is the distance between him and his image now?

A. 1.5 m B. 3 m C. 2 m D. 4 m

30. In a vehicle headlight, the bulb is placed at which position relative to the concave reflector?

A. At the centre of curvature B. Between the pole and the focus C. At the focus D. Beyond the centre of curvature

31. For a real object placed in front of a convex mirror, its image is always:

A. Real, inverted and diminished B. Virtual, erect and enlarged C. Real, erect and of the same size D. Virtual, erect and diminished

32. Match List I (defect of vision) with List II (corrective lens) and select the correct code.
List I:
A. Myopia
B. Hypermetropia
C. Astigmatism
D. Presbyopia (with both near and far defects)
List II:
1. Cylindrical lens
2. Bifocal lens
3. Convex lens
4. Concave lens

A. A-3, B-4, C-1, D-2 B. A-4, B-3, C-2, D-1 C. A-1, B-3, C-4, D-2 D. A-4, B-3, C-1, D-2

33. Match the optical device in List-I with its working feature in List-II.
List-I: A. Simple microscope B. Compound microscope C. Astronomical reflecting telescope D. Optical fibre
List-II: 1. Total internal reflection 2. Large concave mirror that gathers starlight 3. A single convex lens of short focal length 4. Objective and eyepiece, both convex lenses

A. A-4, B-3, C-2, D-1 B. A-3, B-4, C-1, D-2 C. A-2, B-4, C-3, D-1 D. A-3, B-4, C-2, D-1

34. A rainbow is always seen in the part of the sky:

A. In the same direction as the Sun B. Directly overhead at noon C. Only near the northern horizon D. Opposite to the Sun

35. In myopia (short-sightedness), the image of a distant object is formed:

A. Behind the retina B. In front of the retina C. On the blind spot D. On the cornea

36. When a ray of light passes obliquely from air into glass (a denser medium), it:

A. Bends towards the normal B. Bends away from the normal C. Goes straight without bending D. Is totally internally reflected

Answers and explanations

1. C. At sunrise and sunset sunlight passes through a much longer stretch of atmosphere; blue and other short wavelengths are scattered out of the beam, leaving mostly red and orange to reach the eye. The Sun itself does not change.

2. A. In a plane mirror the image is upright, of the same size and as far behind the mirror as the object is in front, but it is laterally inverted: left and right are interchanged. That is why text held before a mirror appears reversed.

3. D. A magnifying glass is a convex (converging) lens of short focal length, thicker at the centre; held close to an object it gives an enlarged, upright image. A concave lens spreads light out and always gives a diminished image.

4. C. A is true under the specified one-wire condition because the potential difference across the bird's close feet is very small, so little current flows through its body. R is false: a bird's body is not a perfect insulator. Contact with another conductor could make the situation very different.

5. A. Violet has a shorter wavelength than blue and is scattered even more, yet sunlight has less violet and our eyes are far less sensitive to it, so the scattered sky light looks blue. Both A and R are true and R explains A.

6. C. Each mirror is inclined at 45° to the tube axis, so light turns through 90° at each mirror: down the tube at the top mirror and into the eye at the bottom mirror. Two reflections let the viewer see over an obstacle.

7. A. Blue sky is linked to scattering (3), rainbow colours to dispersion (4), a hot-road mirage to refraction through air layers with changing refractive properties (2), and a carefully supported needle to surface tension (1). The code is A-3, B-4, C-2, D-1.

8. B. Pressure = force ÷ area = 50 N ÷ 0.01 m² = 5,000 N/m² = 5,000 Pa. The smaller the area, the greater the pressure for the same force, which is why a sharp knife cuts easily and camels have broad feet.

9. D. Light arrives almost instantly, so the delay is the travel time of sound: distance = 340 × 6 = 2,040 m ≈ 2 km. This is the "3 seconds per kilometre" rule. There is no halving here because the sound travels one way only.

10. B. A primary rainbow forms by refraction, one internal reflection and dispersion in raindrops; red appears on the outside and violet on the inside (VIBGYOR from inner to outer). In the fainter secondary rainbow the order is reversed.

11. A. Air near a hot road can have a different temperature and refractive index from the air above. The light path bends through these layers and can reach the eye as if reflected from a surface, giving a watery appearance. There need not be real water on the road, and a sharp interface is not required for the basic refraction explanation.

12. D. Lens power P = 1/f when f is in metres. Here 1/(+0.5 m) = +2 dioptres. A convex converging lens has positive power under the standard sign convention; the unit is the dioptre, or inverse metre.

13. D. Both feet touch the same wire at nearly the same potential, so almost no current flows through the bird. A person touching the wire and the ground bridges a large potential difference, and current passes through the body.

14. A. A fan does not lower air temperature. Moving air sweeps away the moist layer next to the skin, so sweat evaporates faster, and evaporation takes latent heat from the body. Moving heat outside is what a refrigerator or AC does.

15. A. Trapped steam raises the pressure inside, which raises the boiling point to around 120°C. Food cooks faster because the water is hotter, not because of pressure itself. Lower pressure (as on mountains) has the opposite effect.

16. B. Atmospheric pressure falls with altitude, so water boils below 100°C, sometimes under 90°C. The water does boil, but at too low a temperature to cook rice properly. This is the pressure-cooker principle in reverse.

17. D. Glare from a horizontal wet road or water surface is often strongly horizontally polarised. Sunglasses whose transmission axis is vertical suppress much of this reflected component. Real lenses and reflections are not perfectly one-polarisation-only, so 'preferentially' is more accurate than 'only'.

18. D. For a fixed incident ray, rotating a plane mirror by angle θ turns its normal by θ and the reflected ray by 2θ. With θ=10°, the reflected direction changes by 20°. The relation follows from equal incidence and reflection angles.

19. A. Pressure = Force ÷ Area. The camel's weight (the force) stays the same, but broad feet spread it over a larger area, so the pressure on the sand falls and the feet do not sink. The same idea explains wide tyres on heavy vehicles, while a sharp knife works the opposite way (small area, high pressure).

20. D. For a given transmitted power, raising line voltage reduces current and therefore resistive I²R loss. Conventional transformers can efficiently step AC voltage up and down. This explains the stated AC-system design; modern HVDC transmission also exists, so it would be false to claim all long-distance power must be AC.

21. A. A dentist's mirror is a small concave mirror: held close to an object, a concave mirror gives an enlarged, upright image. A convex mirror gives a diminished image and a plane mirror gives an image of the same size as the object.

22. A. Statement I is correct: this is Archimedes' principle; the ship's shape, not its material, lets it displace enough water. Statement II is wrong: a needle floats only because of surface tension, and sinks once the surface film is broken.

23. C. A thermos works by blocking heat transfer (vacuum and silvered walls), not by evaporation. A matka cools as water seeps and evaporates from its porous walls, sweat cools skin, and a fridge's refrigerant absorbs heat as it evaporates inside.

24. A. Sunlight is first refracted and dispersed on entering the drop, then reflected internally at the back surface, and finally refracted again as it exits toward the observer. So the order is C, A, B; neither reflection nor refraction alone makes a rainbow.

25. B. A compound microscope uses two convex lenses: the objective near the specimen forms a magnified image, which the eyepiece magnifies further. A simple microscope has just one convex lens.

26. A. At normal incidence, the angle of incidence is zero, so the refracted direction remains along the normal. Light travels at a different speed in glass than in air. A change in speed does not require a visible change of direction when the ray enters normally.

27. C. Big research telescopes are reflecting telescopes: a large concave mirror collects and focuses far more light than a lens of practical size. Convex mirrors and concave lenses diverge light, so they cannot gather it to a focus.

28. B. Light inside the glass core strikes the core–cladding boundary at angles greater than the critical angle and is totally reflected again and again, so it travels long distances with little loss. The same effect makes diamonds sparkle.

29. B. A plane mirror forms an image as far behind the mirror as the object is in front. After walking 0.5 m the boy is 1.5 m from the mirror, so the image is 1.5 m behind it and the separation is 1.5 + 1.5 = 3 m. Before he walked it was 4 m.

30. C. Rays from a source at the focus of a concave mirror become parallel after reflection, so the headlight throws a strong, parallel beam. A source at the centre of curvature would reflect back on itself.

31. D. Whatever the object position, a convex mirror forms a virtual, erect and diminished image behind the mirror. This, plus its wide field of view, makes it ideal for rear-view and shop security mirrors.

32. D. Myopia is corrected by a concave lens, hypermetropia by a convex lens, astigmatism (irregular corneal curvature) by a cylindrical lens, and presbyopia involving both near and far problems by bifocal lenses. Code: A-4, B-3, C-1, D-2.

33. D. A simple microscope is a single short-focal-length convex lens; a compound microscope uses two convex lenses, an objective and an eyepiece; large astronomical telescopes use big concave mirrors to gather faint starlight; and an optical fibre works by total internal reflection. Hence A-3, B-4, C-2, D-1.

34. D. Sunlight enters raindrops, is refracted, reflected internally and refracted again, and returns toward the observer. So the observer must have the Sun behind them: a rainbow appears opposite the Sun, usually when the Sun is low after rain.

35. B. In myopia the eyeball is too long or the lens too curved, so distant objects focus in front of the retina and look blurred. A concave lens corrects it. In hypermetropia the image of near objects forms behind the retina.

36. A. Light slows down in a denser medium, so on entering glass at an angle it bends toward the normal. Going from denser to rarer it bends away from the normal; total internal reflection happens only when light travels from denser to rarer.