Senior 3 practice book · Unit 8 of 10

Refraction of Light

50 questions that complete the Senior 3 quiz for this unit: 24 core and 26 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

Light bends because the boundary between air and glass pushes or pulls it.Light bends because its SPEED changes when it enters a new medium at an angle; a ray along the normal changes speed but does not bend.
Angles of incidence and refraction are measured from the surface of the glass.All angles in refraction are measured from the NORMAL, the line at 90° to the surface at the point where the ray meets it.
Total internal reflection can happen whenever light hits a surface at a large angle.It happens only when light travels from a denser to a less dense medium (for example glass to air) AND the angle of incidence is greater than the critical angle.
A converging lens always makes things look bigger.The image depends on where the object is: beyond 2F the real image is smaller than the object, at 2F it is the same size, and only between F and 2F (real) or inside F (virtual) is it larger.
A diverging lens has a positive power, like any lens that 'works'.Diverging lenses have a negative focal length, so their power P = 1/f is negative, for example −2.0 D for f = −0.50 m.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Refraction: meaning, cause (change of speed) and bending towards or away from the normal
Laws of refraction, Snell's law and refractive index (n = sin i / sin r = c/v)
Refraction between two media (n₁ sin θ₁ = n₂ sin θ₂) and speed of light in a medium
Critical angle and total internal reflection
Applications of total internal reflection: optical fibres, endoscopes, prisms, diamonds
Parallel-sided glass block: emergent ray and lateral displacement
Real and apparent depth (n = real depth ÷ apparent depth)
Lens terms and ray diagrams: optical centre, principal axis, principal focus, focal length, standard rays
Lens formula 1/f = 1/u + 1/v, magnification and the nature of images
Power of a lens in dioptres
Uses of lenses: the eye, short and long sight, camera, magnifying glass, projector
Dispersion of white light by a prism, the spectrum and rainbows
Experiments: verifying Snell's law with a block and pins, finding the focal length of a lens

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 26 harder ones are marked ★ Challenge.

1True or false
To a person standing on the bank, a fish in a clear pond appears to be deeper than it really is.
Show answer
Answer: False
Light from the fish bends away from the normal as it leaves the water, so the fish appears nearer the surface (shallower) than it really is.
Common mistakeLearners sometimes reverse the effect; remember that pools look shallower than they are, which is why people misjudge their depth.
2True or false · ★ Challenge
If a second prism, turned the other way up, is placed after the first, the band of colours can be joined back into white light.
Show answer
Answer: True
The second prism bends each colour back by the same amount, so the colours overlap again, showing that white light is a mixture of colours.
Common mistakeLearners may think the prism 'adds' colour to light; the colours were already in white light and can be recombined.
3True or false · ★ Challenge
For a diverging lens, rays parallel to the principal axis spread out after the lens as if they came from a principal focus on the same side as the incoming light.
Show answer
Answer: True
The principal focus of a diverging lens is virtual: the rays do not meet but appear to come from F.
Common mistakeLearners sometimes draw the rays of a diverging lens meeting at F on the far side; that is the behaviour of a converging lens.
4True or false
Both a camera and the eye form a real, inverted image on a light-sensitive surface (the sensor or film, and the retina).
Show answer
Answer: True
Each uses a converging lens with the object far away, giving a small real image that can be recorded.
Common mistakeSome learners think the eye's image is virtual; a virtual image cannot be formed on a surface such as the retina.
5True or false
A material with a larger refractive index has a smaller critical angle.
Show answer
Answer: True
sin C = 1/n: as n increases, sin C and therefore C decrease (glass about 42°, diamond about 24°).
Common mistakeLearners sometimes think a 'stronger' material needs a larger angle; it is the other way round.
6True or false · ★ Challenge
When light passes from air into glass, its frequency stays the same while its speed and wavelength both decrease.
Show answer
Answer: True
The frequency is fixed by the source; since v = fλ and v falls, λ must fall by the same factor.
Common mistakeMany learners think the frequency (colour) changes in glass; the colour of light does not change when it enters glass.
7Multiple choice · ★ Challenge
A magnifying glass gives an upright, enlarged image of an insect. Where must the insect be placed?
1. AExactly at the principal focus of the lens
2. BBetween F and 2F on the other side
3. CFurther from the lens than 2F
4. DBetween the lens and its principal focus
Show answer
Answer: D. Between the lens and its principal focus
With u less than f, a converging lens forms a virtual, upright, magnified image on the same side as the object.
Common mistakeChoosing 'between F and 2F' gives a magnified image, but it is real and inverted and would be on the far side of the lens.
8True or false
The larger the refractive index of a material, the more it slows light down.
Show answer
Answer: True
n = c/v, so a larger n means a smaller speed v in the material.
Common mistakeSome learners think a higher n means faster light; n and the speed are inversely related.
9Multiple choice · ★ Challenge
Which change makes the sideways shift (lateral displacement) of a ray passing through a parallel-sided glass block larger?
1. AUsing a thinner block of the same glass
2. BUsing a thicker block of the same glass
3. CMaking the ray strike along the normal
4. DUsing a block with a smaller refractive index
Show answer
Answer: B. Using a thicker block of the same glass
The ray travels further inside a thicker block at its refracted angle, so it ends up further from the line of the incident ray.
Common mistakeChoosing 'along the normal' is the opposite: at normal incidence the ray is not bent, so there is no lateral displacement at all.
10True or false
A ray that strikes a parallel-sided glass block along the normal passes through with no lateral displacement.
Show answer
Answer: True
With i = 0° there is no bending at either face, so the ray continues in the same straight line.
Common mistakeLearners sometimes think every ray through a block is shifted; a shift needs bending, and a ray along the normal does not bend.
11Fill in the blank · ★ Challenge
A ray strikes one face of a parallel-sided glass block at an angle of incidence of 40°. It leaves the opposite face at an angle of ______° to the normal.
Show answer
Answer: 40
Refraction at the second face exactly reverses the bending at the first, so the emergent ray is parallel to the incident ray and makes the same angle, 40°.
Common mistakeLearners often give the angle of refraction inside the glass; the emergent ray is back in air, so its angle equals the original angle of incidence.
12Fill in the blank
The distance from the optical centre of a lens to its principal focus is called the ______ length.
Show answer
Answer: focal
Focal length f; a shorter focal length means a more strongly converging (more powerful) lens.
Common mistakeSome learners measure from the edge of the lens; f is measured from the optical centre.
13Multiple choice
The image formed on the retina of a healthy human eye is:
1. AVirtual, upright and magnified
2. BReal, upside down and diminished
3. CReal, upright and the same size
4. DVirtual, inverted and diminished
Show answer
Answer: B. Real, upside down and diminished
The eye lens acts like a converging lens with the object far beyond 2F, so it forms a small, real, upside-down image; the brain interprets it the right way up.
Common mistakeChoosing 'upright' assumes we see the image the way it is formed; the retinal image is inverted and the brain corrects it.
14Multiple choice · ★ Challenge
A ray from the top of an object travels parallel to the principal axis and passes through a CONVERGING lens. After the lens, it:
1. APasses through the principal focus on the far side
2. BContinues parallel to the principal axis
3. CSeems to come from the principal focus on the object side
4. DPasses back through the top of the object
Show answer
Answer: A. Passes through the principal focus on the far side
A converging lens bends rays that are parallel to the axis so that they pass through F on the far side.
Common mistakeChoosing 'seems to come from the focus on the object side' is the rule for a DIVERGING lens, whose parallel rays spread out.
15Multiple choice · ★ Challenge
A ray of light passes at an angle from a glass block out into the air. What happens to its speed and direction?
1. AIt slows down and bends towards the normal
2. BIt speeds up and bends towards the normal
3. CIt speeds up and bends away from the normal
4. DIt slows down and bends away from the normal
Show answer
Answer: C. It speeds up and bends away from the normal
Air is optically less dense than glass, so light travels faster in air and bends away from the normal as it leaves the glass.
Common mistakeChoosing 'speeds up and bends towards the normal' mixes the rules: faster means bending AWAY from the normal.
16Multiple choice
The principal focus of a converging lens is the point where:
1. AThe principal axis crosses the surface of the lens
2. BRays through the optical centre are bent the most
3. CRays parallel to the principal axis meet after the lens
4. DThe image of any object is always formed
Show answer
Answer: C. Rays parallel to the principal axis meet after the lens
Parallel rays close to the principal axis are all brought together at one point, the principal focus F, on the far side of the lens.
Common mistakeChoosing 'the image is always formed there' is wrong: only very distant objects form their image at F; nearer objects form images further away.
17Multiple choice · ★ Challenge
Good binoculars use right-angled glass prisms instead of plane mirrors to turn the light. Why are prisms better?
1. AThey reflect nearly all the light and do not tarnish
2. BThey magnify the image more than a mirror does
3. CThey split the light into colours for a sharper view
4. DThey let light pass straight through without bending
Show answer
Answer: A. They reflect nearly all the light and do not tarnish
Total internal reflection sends back almost 100 % of the light, and there is no silver coating to fade or give a faint double image.
Common mistakeChoosing 'they magnify the image' gives the job of the lenses to the prisms; the prisms only turn the light.
18Fill in the blank
Refractive index has no ______ because it is the ratio of two speeds (or of the sines of two angles).
Show answer
Answer: unit
n = c/v: metres per second divided by metres per second leaves a pure number.
Common mistakeSome learners give the refractive index in m/s or degrees; it is a number without a unit.
19Short answer · ★ Challenge
In a glass-block-and-pins experiment to check Snell's law, suggest two precautions that make the results more accurate.
Show answer
Model answer: Any two: place the pins upright and at least 5 cm apart so the ray direction is accurate; line up the bottoms of the pins (not the tops) when looking through the block; draw thin lines with a sharp pencil; draw the normal carefully at 90° and measure every angle from it; take readings for a wide range of angles of incidence and repeat them.
Common mistakeMany learners place the pins very close together; small errors in pin position then give large errors in the angle.
20Multiple choice
Doctors use an endoscope, made of bundles of optical fibres, mainly to:
1. AKill germs with strong ultraviolet light
2. BTake X-ray pictures of broken bones inside the body
3. CSee inside the body through a small opening
4. DMeasure the temperature inside organs
Show answer
Answer: C. See inside the body through a small opening
Light is carried into the body along some fibres and the image is carried back along others by total internal reflection, so no large cut is needed.
Common mistakeChoosing X-ray pictures confuses two different tools; an endoscope uses visible light guided by optical fibres.
21Multiple choice · ★ Challenge
A transparent material has a critical angle of 30° with air. What is its refractive index?
1. A0.50
2. B2.00
3. C1.15
4. D1.73
Show answer
Answer: B. 2.00
sin C = 1/n, so n = 1 ÷ sin 30° = 1 ÷ 0.50 = 2.0.
Common mistakeChoosing 0.50 stops at sin 30°; that is 1/n, so it must be turned upside down to give n.
22Fill in the blank
When looking for the image of a pin, a search pin is in the right place when there is no ______ between it and the image as you move your head from side to side.
Show answer
Answer: parallax
With no parallax, the search pin and the image stay lined up when the eye moves, so they are at the same place.
Common mistakeSome learners write 'gap'; the correct term is parallax, the apparent relative movement of two objects at different distances.
23Multiple choice · ★ Challenge
Looking straight down into a clear water tank at a school, the bottom appears to be 0.90 m below the surface. The refractive index of water is 1.33. What is the real depth?
1. A0.68 m
2. B0.90 m
3. C2.2 m
4. D1.2 m
Show answer
Answer: D. 1.2 m
n = real depth ÷ apparent depth, so real depth = 1.33 × 0.90 = 1.2 m.
Common mistakeChoosing 0.68 m divides by n; the real depth must be GREATER than the apparent depth, so multiply.
24Multiple choice
In a ray diagram, a ray passing through the optical centre of a thin lens:
1. AIs bent to pass through the principal focus
2. BComes out parallel to the principal axis
3. CGoes straight on without changing direction
4. DIs reflected back towards the object
Show answer
Answer: C. Goes straight on without changing direction
Near its centre a thin lens is like a thin parallel-sided block, so the ray is not deviated.
Common mistakeChoosing 'bent through the principal focus' describes the ray that started PARALLEL to the axis, not the ray through the centre.
25Multiple choice · ★ Challenge
A converging lens forms a real image three times the size of the object, 40 cm from the lens. What is the focal length of the lens?
1. A13 cm
2. B10 cm
3. C30 cm
4. D120 cm
Show answer
Answer: B. 10 cm
u = v ÷ m = 40 ÷ 3 = 13.3 cm. 1/f = 1/13.3 + 1/40 = 3/40 + 1/40 = 4/40, so f = 10 cm.
Common mistakeChoosing 13 cm gives the object distance, not the focal length; you must still use the lens formula.
26Short answer · ★ Challenge
A triangular glass prism splits white light into clear colours, but a parallel-sided glass block hardly shows any colours. Explain the difference.
Show answer
Model answer: In both, the colours are refracted by slightly different amounts at the first face. In the block the second face is parallel to the first, so each colour is bent back by the same amount and leaves parallel to the others; the colours overlap and the light still looks white. In a prism the faces are not parallel, so the second face bends the colours even further apart.
Common mistakeLearners often say glass blocks 'do not cause dispersion'; dispersion happens at the first face of both, but the block cancels it at the second face.
27Multiple choice
You see a rainbow in the spray from a waterfall on a sunny afternoon. Where must the Sun be?
1. AIn front of you, just behind the spray itself
2. BBehind you, shining towards the spray
3. CDirectly overhead at midday
4. DBelow the horizon, out of sight
Show answer
Answer: B. Behind you, shining towards the spray
Light enters the drops, is refracted, reflected inside and refracted again on leaving, coming back towards the side the light came from, so the Sun must be behind the observer.
Common mistakeChoosing 'in front of you, behind the spray' assumes the light passes straight through the drops; the internal reflection sends it back towards you.
28Multiple choice
Which equation gives the refractive index of a liquid from depths measured by looking vertically down?
1. An = real depth ÷ apparent depth
2. Bn = apparent depth ÷ real depth
3. Cn = real depth − apparent depth
4. Dn = real depth × apparent depth
Show answer
Answer: A. n = real depth ÷ apparent depth
The bottom appears raised, so the real depth is larger; their ratio, real ÷ apparent, gives n (greater than 1).
Common mistakeChoosing apparent ÷ real gives a value below 1, which is impossible for a refractive index.
29Multiple choice · ★ Challenge
Two thin lenses of power +5.0 D and −2.0 D are placed in contact. Powers of thin lenses in contact add. What is the focal length of the combination?
1. A+14 cm
2. B−33 cm
3. C+33 cm
4. D+3.0 cm
Show answer
Answer: C. +33 cm
P = +5.0 + (−2.0) = +3.0 D, so f = 1 ÷ 3.0 = 0.33 m = +33 cm (converging).
Common mistakeChoosing +14 cm adds 5 + 2 = 7 D and ignores the minus sign of the diverging lens.
30Multiple choice
A learner can read her book clearly but cannot see the writing on the board at the back of the class. Which lens corrects her sight?
1. AA converging (convex) lens
2. BA parallel-sided glass block
3. CA right-angled glass prism
4. DA diverging (concave) lens
Show answer
Answer: D. A diverging (concave) lens
She is short-sighted: light from distant objects is focused in front of the retina. A diverging lens spreads the rays a little so they focus on the retina.
Common mistakeChoosing a converging lens is a common mix-up; converging lenses correct LONG sight, where near objects are blurred.
31Multiple choice · ★ Challenge
Light travels at 2.25 × 10⁸ m/s in water and at 2.0 × 10⁸ m/s in a type of glass. What is the refractive index for light going from the water into this glass?
1. A0.89
2. B1.50
3. C1.33
4. D1.13
Show answer
Answer: D. 1.13
Relative index = speed in first medium ÷ speed in second = 2.25 × 10⁸ ÷ 2.0 × 10⁸ = 1.13.
Common mistakeChoosing 1.50 gives the index of the glass relative to AIR; going from water, compare with the speed in water, not in air.
32True or false
If an object is placed exactly at the principal focus of a converging lens, the refracted rays come out parallel and no image can be caught on a screen.
Show answer
Answer: True
With u = f, 1/v = 1/f − 1/f = 0, so v is infinitely large: the image is 'at infinity'.
Common mistakeLearners may expect a very large image close to the lens; in fact no image forms at any finite distance.
33Short answer · ★ Challenge
A grandmother sees distant hills clearly but cannot read a newspaper held at a normal distance. Name her sight defect, explain what happens to the light from the newspaper inside her eye, and state the type of lens that corrects it.
Show answer
Model answer: She is long-sighted. The eye lens cannot converge the light from near objects enough (it has become less flexible with age), so the image would be formed behind the retina and is blurred. A converging (convex) lens adds extra converging power so that the image falls on the retina.
Common mistakeLearners often say the image forms 'in front of' the retina; that is short sight, which is corrected with a diverging lens.
34Multiple choice · ★ Challenge
With a converging lens, a learner records object and image distances: u = 30 cm, v = 15 cm; u = 20 cm, v = 20 cm; u = 15 cm, v = 30 cm. What is the focal length?
1. A20 cm
2. B45 cm
3. C10 cm
4. D15 cm
Show answer
Answer: C. 10 cm
f = uv ÷ (u + v): 30 × 15 ÷ 45 = 10 cm, 20 × 20 ÷ 40 = 10 cm and 15 × 30 ÷ 45 = 10 cm. When u = v the object is at 2F, so f = 20 ÷ 2 = 10 cm.
Common mistakeChoosing 20 cm takes the u = v reading as f; when u = v = 20 cm the object is at 2F, so f is half of 20 cm.
35Fill in the blank
A lens whose power is −4.0 D is a ______ lens.
Show answer
Answer: diverging (concave)
f = 1/P = 1 ÷ (−4.0) = −0.25 m; a negative focal length belongs to a diverging lens.
Common mistakeSome learners ignore the sign and call any lens of 4 D converging; the minus sign tells you it is diverging.
36Short answer · ★ Challenge
Describe how to draw a ray diagram to find the image of an object placed between the principal focus F and a converging lens, and state the nature of the image.
Show answer
Model answer: From the top of the object draw one ray parallel to the principal axis, bent through F on the far side, and a second ray straight through the optical centre. These two rays spread apart after the lens, so extend them backwards with dotted lines until they meet on the object side. The image is there: virtual, upright and magnified.
Common mistakeLearners often look for the image on the far side; when u is less than f the refracted rays never meet, so the image is found by tracing them back.
37Multiple choice
A ray travels at an angle from crown glass (n = 1.52) into water (n = 1.33). How does it bend?
1. ATowards the normal, as water is less dense
2. BIt does not bend at all, as both are transparent
3. CTowards the normal, as water is more dense
4. DAway from the normal, as water is less dense
Show answer
Answer: D. Away from the normal, as water is less dense
Water has the smaller refractive index, so light speeds up on entering it and bends away from the normal.
Common mistakeChoosing 'it does not bend' assumes refraction happens only at air boundaries; any change in refractive index makes the ray bend.
38Multiple choice · ★ Challenge
To show from experimental results that sin i ÷ sin r is constant for a glass block, which graph should a learner plot?
1. Asin i against sin r: a straight line through the origin
2. Bi against r: a straight line through the origin
3. Csin i against r: a straight line with no intercept at all
4. Di against sin r: a curve rising to a maximum
Show answer
Answer: A. sin i against sin r: a straight line through the origin
If sin i = n sin r, a graph of sin i against sin r is a straight line through the origin whose gradient is n.
Common mistakeChoosing i against r assumes the angles themselves are proportional; only their sines are, so the i–r graph curves at large angles.
39Multiple choice
Why does a ray of light change direction when it enters a glass block at an angle?
1. AIts speed changes as it crosses into the glass
2. BIt is partly reflected from the glass surface
3. CThe glass attracts the light towards the normal
4. DIts frequency changes as it crosses the surface
Show answer
Answer: A. Its speed changes as it crosses into the glass
Light travels more slowly in glass than in air. Hitting the surface at an angle, one side of the beam slows down first, so the beam swings round and changes direction.
Common mistakeChoosing 'the glass attracts the light' gives a force-based picture; the bending is caused only by the change of speed.
40Multiple choice · ★ Challenge
A converging lens of focal length 10 cm forms a real image exactly the same size as the object. How far is the object from the lens?
1. A10 cm
2. B5.0 cm
3. C40 cm
4. D20 cm
Show answer
Answer: D. 20 cm
Same size means m = v/u = 1, so v = u. Then 1/10 = 1/u + 1/u = 2/u, giving u = 20 cm (at 2F).
Common mistakeChoosing 10 cm puts the object at F, where no image forms on a screen; a same-size image needs the object at 2F.
41Multiple choice
A lens has a power of +2.5 D. What are its focal length and type?
1. A40 cm, converging
2. B2.5 cm, converging
3. C40 cm, diverging
4. D25 cm, converging
Show answer
Answer: A. 40 cm, converging
f = 1/P = 1 ÷ 2.5 = 0.40 m = 40 cm. A positive power means a converging lens.
Common mistakeChoosing '40 cm, diverging' ignores the sign; a + power is a converging lens and a − power is diverging.
42Short answer · ★ Challenge
Diamond has a refractive index of 2.42 (critical angle about 24°), while ordinary glass has 1.5 (critical angle about 42°). Use these values to explain why a cut diamond sparkles far more than a glass copy of the same shape.
Show answer
Model answer: Because diamond's critical angle is so small, most rays inside it meet the faces at more than 24° and are totally internally reflected many times before they leave through the top. In glass, with a 42° critical angle, many rays escape through the back and sides, so less light comes back to the eye.
Common mistakeA common error is to say diamond 'produces' light; it only traps and redirects light from outside by total internal reflection.
43Short answer
Both the eye and a camera can focus on near and on distant objects. Explain how each one does it.
Show answer
Model answer: The eye changes the SHAPE of its lens: the ciliary muscles make the lens fatter (shorter focal length) for near objects and thinner for distant ones, while the lens-to-retina distance stays fixed. A camera keeps the same lens but MOVES it further from the sensor for near objects and closer for distant ones.
Common mistakeLearners often say the eye moves its lens backwards and forwards; it changes the focal length instead.
44Multiple choice · ★ Challenge
A learner plots sin i (y-axis) against sin r (x-axis) for light entering a plastic block. She gets a straight line through the origin that passes through the point (0.50, 0.75). What is the refractive index of the plastic?
1. A0.67
2. B1.50
3. C0.25
4. D1.25
Show answer
Answer: B. 1.50
For a straight line through the origin, n = sin i ÷ sin r = gradient = 0.75 ÷ 0.50 = 1.5.
Common mistakeChoosing 0.67 divides x by y (0.50 ÷ 0.75); with sin i on the y-axis the gradient is sin i ÷ sin r.
45Short answer
A straight pencil stands at an angle in a glass of water. Seen from the side and above, it looks bent at the water surface. Explain why.
Show answer
Model answer: Light from the part of the pencil under water bends away from the normal as it leaves the water. The eye traces the rays back in straight lines, so the underwater part appears higher (shallower) than it really is, and the pencil looks bent at the surface.
Common mistakeLearners sometimes say the water bends the pencil itself; only the light rays are bent, the pencil stays straight.
46Short answer · ★ Challenge
A learner measures the angles between the rays and the SURFACE of a glass block: the incident ray makes 60° with the surface and the refracted ray makes 70° with the surface. She writes n = sin 60° ÷ sin 70° = 0.92 and concludes that glass is less optically dense than air. Correct her working.
Show answer
Model answer: Angles must be measured from the normal: i = 90° − 60° = 30° and r = 90° − 70° = 20°. n = sin 30° ÷ sin 20° = 0.500 ÷ 0.342 = 1.46, which is greater than 1, as expected for glass.
Common mistakeThe error is measuring from the surface; a refractive index below 1 for glass should warn you that the angles are wrong.
47Short answer
Describe a quick way to find the approximate focal length of a converging lens using a distant tree or window.
Show answer
Model answer: Hold the lens so that light from the distant object passes through it onto a white wall or screen. Move the lens until a sharp, small, inverted image appears. Measure the distance from the lens to the screen: this is approximately the focal length, because rays from a very distant object are almost parallel and meet at F.
Common mistakeLearners sometimes use a nearby object such as a lamp on the bench; the object must be far away, or the image forms beyond F and the value is too large.
48Short answer · ★ Challenge
The lens of a school projector has a focal length of 12 cm. It forms a sharp image of a slide on a screen 3.0 m from the lens. Calculate the distance of the slide from the lens and the magnification.
Show answer
Model answer: v = 300 cm. 1/u = 1/f − 1/v = 1/12 − 1/300 = 25/300 − 1/300 = 24/300, so u = 12.5 cm. m = v/u = 300 ÷ 12.5 = 24.
Common mistakeLearners often forget to change 3.0 m into 300 cm, mixing metres and centimetres in the same formula.
49Short answer · ★ Challenge
A ray of light in air meets a layer of cooking oil (n = 1.45) floating on water (n = 1.33) at an angle of incidence of 45°. It passes through the oil into the water. Calculate the angle of refraction in the water.
Show answer
Model answer: n sin θ is the same at every parallel boundary: 1.00 × sin 45° = 1.33 × sin θ, so sin θ = 0.707 ÷ 1.33 = 0.532 and θ = 32.1°. The oil layer does not change the final angle.
Common mistakeLearners often work out the angle in the oil and then wrongly use n = 1.33 alone at the oil–water boundary; use n₁ sin θ₁ = n₂ sin θ₂ with BOTH indices.
50Short answer
A ray inside a glass block (critical angle 42°) meets the glass–air surface. Describe what happens as its angle of incidence is slowly increased from 0° to 60°.
Show answer
Model answer: At 0° it passes straight out. As the angle increases, the ray refracts out, bending away from the normal, with a weak reflected ray. At 42° the refracted ray runs along the surface (angle of refraction 90°). Above 42° no light leaves: all of it is reflected back into the glass (total internal reflection), and the reflected ray becomes bright.
Common mistakeLearners often say there is no reflection at all below the critical angle; a weak partial reflection is always present.