Senior 2 practice book · Unit 10 of 10

Reflection of Light in Curved Mirrors

50 questions that complete the Senior 2 quiz for this unit: 26 core and 24 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

The angle of incidence is measured between the ray and the mirror surface.Both angles are measured from the NORMAL; for a curved mirror the normal at a point is the radius through that point (the line to C).
The focal length of a curved mirror equals its radius of curvature.The principal focus is halfway between the pole and the centre of curvature, so f = r/2.
A larger mirror always gives a larger image.The size and position of the image depend on the focal length and the object distance; a larger aperture only collects more light (and can cause spherical aberration).
A virtual image can be caught on a screen if the screen is put in the right place.Rays only APPEAR to come from a virtual image (behind the mirror); they never actually meet there, so no screen can show it.
A negative image distance is a mistake in the calculation.In the real-is-positive convention a negative v simply means the image is virtual, behind the mirror.

What this unit covers

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

Laws of reflection
Plane mirrors: rotating a mirror, images in inclined mirrors, mirror length for a full image
Curved-mirror terms: pole, centre of curvature, principal focus, principal axis, aperture
Relation between focal length and radius of curvature, f = r/2
Rules for drawing rays to concave and convex mirrors
Images formed by a concave mirror for different object positions
Images formed by a convex mirror
Mirror formula 1/f = 1/u + 1/v and the real-is-positive sign convention
Magnification and image height
Locating images by scale ray diagrams
Experimental determination of the focal length of a concave mirror
Spherical aberration and parabolic mirrors
Uses of concave and convex mirrors

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 24 harder ones are marked ★ Challenge.

1True or false
Large telescopes use big concave mirrors to collect light from faint stars.
Show answer
Answer: True
A large concave (usually parabolic) mirror gathers a lot of light and brings it to a focus.
Common mistakeSome think telescopes always use lenses; the biggest telescopes use mirrors.
2True or false · ★ Challenge
A magnification of 0.5 always means the image is real.
Show answer
Answer: False
A convex mirror gives virtual images with magnifications less than 1, e.g. 0.5; m alone does not tell you whether an image is real.
Common mistakeLearners link 'diminished' with 'real' from the concave mirror; convex mirrors give diminished VIRTUAL images.
3True or false
In the real-is-positive convention, a negative image distance means that the image is virtual.
Show answer
Answer: True
Real distances (in front of the mirror) are positive; virtual ones (behind it) are negative.
Common mistakeLearners often think a negative answer means they made a mistake; it tells you the image is virtual.
4True or false · ★ Challenge
The image formed by a convex mirror always lies between the pole and the principal focus, behind the mirror.
Show answer
Answer: True
For any real object, 1/v = 1/f − 1/u with f negative gives v between 0 and f behind the mirror.
Common mistakeSome think a distant object's image can be beyond F; its image approaches F but never passes it.
5True or false
Spherical aberration can be reduced by covering the outer part of a spherical mirror so that only rays near the axis are used.
Show answer
Answer: True
Rays close to the axis (paraxial rays) all meet very nearly at F, so a small aperture gives a sharper image.
Common mistakeLearners think a bigger mirror is always better; a large aperture increases spherical aberration.
6Multiple choice · ★ Challenge
Can a concave mirror form a VIRTUAL image that is SMALLER than the object?
1. ANo: its virtual images are always magnified
2. BYes, when the object is placed exactly at F
3. CYes, when the object is beyond C
4. DYes, when the object is between F and C
Show answer
Answer: A. No: its virtual images are always magnified
A concave mirror forms a virtual image only when the object is inside F, and that image is always upright and magnified.
Common mistake'Yes, beyond C' mixes up concave and convex mirrors: beyond C the image is smaller but real.
7True or false
The laws of reflection apply to curved mirrors as well as to plane mirrors.
Show answer
Answer: True
At each point a curved mirror behaves like a tiny plane mirror; i = r measured from the normal at that point.
Common mistakeSome think curved mirrors 'bend' light by other rules; they obey the same laws, but the normal changes from point to point.
8Multiple choice · ★ Challenge
A large spherical mirror reflects sunlight onto a card. Which observation shows spherical aberration?
1. AA coloured rainbow band spread across the card
2. BA blurred bright patch with a bright curved edge
3. CA tiny, sharp point of light at F
4. DNo light at all on the card
Show answer
Answer: B. A blurred bright patch with a bright curved edge
Edge rays and central rays focus at different distances, so instead of one point a blurred patch with a bright curve (caustic) appears.
Common mistakeA coloured band is caused by lenses splitting light (dispersion), not by mirrors.
9True or false
For a convex mirror, a ray parallel to the principal axis is reflected so that it appears to come from the principal focus behind the mirror.
Show answer
Answer: True
A convex mirror spreads parallel rays out; traced back, they seem to come from the virtual focus behind it.
Common mistakeSome draw the reflected ray passing through F in front of the mirror; for a convex mirror F is BEHIND it.
10Multiple choice · ★ Challenge
A ray strikes a concave mirror exactly at its pole, making an angle of 20° with the principal axis. How does it leave the mirror?
1. AAt 20° to the axis, on the other side of it
2. BParallel to the principal axis afterwards
3. CBack along its own path to the object
4. DThrough the principal focus in front
Show answer
Answer: A. At 20° to the axis, on the other side of it
At the pole the principal axis is the normal, so the ray reflects at the same angle (20°) on the other side of the axis.
Common mistake'Through the principal focus' applies only to rays arriving parallel to the axis.
11True or false
For a concave mirror, the principal focus lies between the pole and the centre of curvature.
Show answer
Answer: True
F is halfway between P and C, since f = r/2.
Common mistakeSome place F beyond C; F is always closer to the mirror than C.
12Fill in the blank
The width of the reflecting surface of a curved mirror is called its ______.
Show answer
Answer: aperture
The aperture is the size (width) of the mirror's reflecting surface.
Common mistakeLearners confuse aperture with focal length; aperture is a width across the mirror, not a distance along the axis.
13Multiple choice · ★ Challenge
In a convex wing mirror, a following car looks further away than it really is. Why?
1. AIts image is real
2. BIts image is formed behind the mirror
3. CIts image is upside down
4. DIts image is smaller than the car
Show answer
Answer: D. Its image is smaller than the car
A convex mirror gives a diminished image; the brain judges the smaller image as being further away.
Common mistake'Its image is behind the mirror' is true but every mirror image is behind the mirror; the SIZE is what misleads.
14Multiple choice · ★ Challenge
In the no-parallax method, a pin and its inverted image coincide exactly when the pin is 30 cm from a concave mirror. What is the focal length?
1. A30 cm
2. B7.5 cm
3. C60 cm
4. D15 cm
Show answer
Answer: D. 15 cm
Object and image coincide only at the centre of curvature, so r = 30 cm and f = r/2 = 15 cm.
Common mistake30 cm treats the coincidence point as F; at F the image would be at infinity.
15Fill in the blank
In the u–v method, the ______ is moved backwards and forwards until a sharp image of the illuminated object is seen on it.
Show answer
Answer: screen
A real image is located where the screen shows it sharply in focus.
Common mistakeSome move the mirror instead and lose track of u; keep u fixed and move the screen.
16Multiple choice · ★ Challenge
A shaving mirror is cut from a hollow glass sphere of diameter 60 cm. What is its focal length?
1. A120 cm
2. B60 cm
3. C30 cm
4. D15 cm
Show answer
Answer: D. 15 cm
r = 60 ÷ 2 = 30 cm, so f = r/2 = 15 cm.
Common mistake30 cm halves only once, treating the diameter as if it were 2f.
17Multiple choice
Which of these is NOT a use of a concave mirror?
1. AA torch reflector
2. BA make-up mirror
3. CA solar cooker dish for heating a pot
4. DA wide-view moto rear-view mirror
Show answer
Answer: D. A wide-view moto rear-view mirror
Rear-view mirrors are convex, to give a wide field of view; the other three use concave mirrors.
Common mistakeA make-up mirror may look flat, but it is concave so that it gives a magnified upright image.
18Multiple choice · ★ Challenge
A shiny steel ball bearing of diameter 2.0 cm acts as a convex mirror. What is the size of its focal length?
1. A2.0 cm
2. B1.0 cm
3. C0.5 cm
4. D4.0 cm
Show answer
Answer: C. 0.5 cm
Radius r = 2.0 ÷ 2 = 1.0 cm; f = r/2 = 0.5 cm (−0.5 cm with the sign convention, as it is convex).
Common mistake1.0 cm uses the diameter as if it were the radius; you must halve twice: diameter → radius → focal length.
19Multiple choice
What is spherical aberration in a large concave spherical mirror?
1. AThe image is laterally inverted
2. BRays near the axis are not reflected at all by the mirror
3. CEdge rays focus nearer the mirror, so the image blurs
4. DAll rays meet exactly at F, making a sharp image
Show answer
Answer: C. Edge rays focus nearer the mirror, so the image blurs
Rays striking far from the axis are reflected to points closer to the mirror than F, so there is no single sharp focus.
Common mistake'All rays meet exactly at F' is what a PARABOLIC mirror does, or a spherical mirror with a small aperture.
20Fill in the blank · ★ Challenge
An object is 20 cm in front of a convex mirror of focal length 20 cm (f = −20 cm). The image is ______ cm behind the mirror.
Show answer
Answer: 10
1/v = 1/f − 1/u = −1/20 − 1/20 = −2/20, so v = −10 cm: 10 cm behind the mirror (virtual).
Common mistakeUsing f = +20 cm gives 1/v = 0 (image at infinity); for a convex mirror f must be negative.
21Multiple choice
A learner wants a concave mirror to throw an enlarged picture of a lamp onto a screen. In which region must the lamp be?
1. AExactly at C
2. BBetween F and C
3. CBetween F and the pole
4. DBeyond C
Show answer
Answer: B. Between F and C
With the object between F and C the image is real, inverted, magnified and beyond C.
Common mistake'Between F and the pole' gives a magnified image, but it is virtual, not real.
22Fill in the blank
A girl stands 2 m in front of a plane mirror. The distance between her and her image is ______ m.
Show answer
Answer: 4
The image is as far behind the mirror as she is in front: 2 + 2 = 4 m.
Common mistakeAnswering 2 m gives the distance from the mirror to the image, not from the girl to her image.
23Multiple choice · ★ Challenge
In a ray diagram, the two reflected rays from the top of an object spread apart after reflection. How do you find the image?
1. AThere is no image when reflected rays spread
2. BExtend them back behind the mirror as dashed lines
3. CKeep drawing more rays until two of them finally cross
4. DMove the object until the rays meet
Show answer
Answer: B. Extend them back behind the mirror as dashed lines
Diverging rays never meet in front of the mirror; extended backwards (dashed) they meet behind it, at a virtual image.
Common mistake'There is no image' forgets virtual images: the eye sees an image where the rays seem to come from.
24Fill in the blank
If the magnification produced by a mirror is 1, the image is the same ______ as the object.
Show answer
Answer: size
m = image height ÷ object height = 1 means equal heights.
Common mistakeSome answer 'distance'; m = 1 does give v = u, but the word asked about is size.
25Short answer · ★ Challenge
Explain why the upright image of a candle placed between a concave mirror and its principal focus cannot be caught on a screen.
Show answer
Model answer: With the candle inside F the reflected rays spread out (diverge) and never actually meet in front of the mirror. They only appear to come from a point behind the mirror, so the image is virtual. A screen shows an image only where light rays really meet, so this image cannot be caught on a screen.
Common mistakeSome say the screen is just in the wrong place; there is NO position where the rays meet.
26Multiple choice
A plane mirror is turned through 10° while the incident ray stays fixed. Through what angle does the reflected ray turn?
1. A40°
2. B5°
3. C20°
4. D10°
Show answer
Answer: C. 20°
Turning the mirror by θ changes both i and r by θ, so the reflected ray turns through 2θ = 20°.
Common mistake10° assumes the ray turns with the mirror; both angles change, so the ray turns twice as much.
27Multiple choice · ★ Challenge
A pupil holds a concave mirror of focal length 25 cm so that it faces a candle 75 cm away. Where must she hold a sheet of paper to see a sharp image of the flame?
1. A50 cm from the mirror
2. B37.5 cm from the mirror
3. C100 cm from the mirror
4. D18.8 cm from the mirror
Show answer
Answer: B. 37.5 cm from the mirror
1/v = 1/f − 1/u = 1/25 − 1/75 = 2/75, so v = 37.5 cm in front of the mirror (real image).
Common mistake18.8 cm adds 1/25 and 1/75 instead of subtracting; 50 cm simply subtracts the distances (u − f).
28Multiple choice
An object moves from far away towards a convex mirror. What happens to its image?
1. AIt moves away from the mirror and shrinks
2. BIt stays virtual, moves towards the mirror and grows
3. CIt changes from a real image to a virtual one
4. DIt turns upside down once the object is near
Show answer
Answer: B. It stays virtual, moves towards the mirror and grows
A convex mirror always forms a virtual upright diminished image between P and F; as the object approaches, the image moves from F towards P and gets larger (but stays smaller than the object).
Common mistake'Changes from real to virtual' describes a concave mirror; a convex mirror never forms a real image.
29Multiple choice · ★ Challenge
Where must an object be placed in front of a concave mirror (f = 10 cm) to form a virtual image 30 cm behind the mirror?
1. A40 cm
2. B10.0 cm
3. C15 cm
4. D7.5 cm
Show answer
Answer: D. 7.5 cm
v = −30 cm (virtual). 1/u = 1/f − 1/v = 1/10 + 1/30 = 4/30, so u = 7.5 cm (inside F, as expected).
Common mistake15 cm uses v = +30 cm, forgetting that a virtual image has a NEGATIVE image distance.
30Fill in the blank
To get a real image the same size as the object from a concave mirror of focal length 8 cm, the object must be placed ______ cm from the mirror.
Show answer
Answer: 16
Same-size real image when the object is at C, i.e. u = r = 2f = 16 cm.
Common mistakeAnswering 8 cm places the object at F, which sends the image to infinity.
31Short answer · ★ Challenge
What is the shortest vertical plane mirror in which a man 1.6 m tall can see his whole body? Explain.
Show answer
Model answer: 0.8 m, half his height. Light from his feet reflects to his eyes from a point halfway between eye level and his feet, and light from the top of his head reflects from a point halfway between his eyes and the top of his head, so the mirror needs to cover half his height (placed correctly), whatever his distance from it.
Common mistakeMany think the mirror must be as tall as the person, or that standing further back helps; neither is true.
32True or false
In a ray diagram, a virtual image is drawn where the reflected rays actually cross in front of the mirror.
Show answer
Answer: False
A virtual image is where the reflected rays, extended BACKWARDS behind the mirror, appear to meet.
Common mistakeMixing up real and virtual images in diagrams is common; real rays cross only for real images.
33Short answer · ★ Challenge
Satellite TV dishes and solar cookers are made parabolic rather than spherical. Explain what would happen to the signal at the receiver if a wide spherical dish were used instead.
Show answer
Model answer: A wide spherical dish suffers from spherical aberration: signals reaching the outer parts of the dish are reflected to points nearer the dish than the focus, so they do not all meet at the receiver. The energy is spread over a region instead of a point, so the signal at the receiver is weaker. A parabolic dish brings all parallel rays, even at the edges, to one focus.
Common mistakeSome say a spherical dish has no focus at all; it has a focus for rays near the axis, but edge rays miss it.
34Multiple choice
In the real-is-positive sign convention, what sign is given to the focal length of a convex mirror, and why?
1. APositive, as its focus is in front of it
2. BNegative, as it makes inverted images
3. CPositive, as all focal lengths are taken as positive
4. DNegative, as its focus is virtual, behind it
Show answer
Answer: D. Negative, as its focus is virtual, behind it
The principal focus of a convex mirror is behind the mirror (virtual), so f is negative.
Common mistake'Negative, as it makes inverted images' gives the right sign for the wrong reason: convex mirrors form upright images.
35Multiple choice · ★ Challenge
Two plane mirrors are placed at 60° to each other with a coin between them. How many images of the coin are seen?
1. A3
2. B6
3. C5
4. D4
Show answer
Answer: C. 5
n = 360° ÷ θ − 1 = 360 ÷ 60 − 1 = 5.
Common mistake6 forgets to subtract 1; the coin itself occupies one of the 6 positions.
36Multiple choice
A 6.0 cm tall object gives an image 1.5 cm tall. What is the magnification?
1. A0.25
2. B4.0
3. C7.5
4. D4.5
Show answer
Answer: A. 0.25
m = image height ÷ object height = 1.5 ÷ 6.0 = 0.25.
Common mistake4 divides the object height by the image height; magnification is IMAGE ÷ object.
37Short answer · ★ Challenge
A ray of light strikes a concave mirror at a point X away from the pole. Explain how you would find the normal at X and draw the reflected ray.
Show answer
Model answer: The normal at any point of a spherical mirror is the radius through that point, so draw a line from the centre of curvature C to X. Measure the angle of incidence between the incident ray and this line, then draw the reflected ray on the other side of the normal at an equal angle (i = r).
Common mistakeA frequent error is to draw the normal at right angles to the principal axis; it must go through C.
38Multiple choice
A ray strikes a plane mirror with an angle of incidence of 35°. What is the angle between the incident ray and the reflected ray?
1. A70°
2. B55°
3. C35°
4. D110°
Show answer
Answer: A. 70°
r = i = 35°, and both are measured from the normal on opposite sides, so the angle between the rays = 35° + 35° = 70°.
Common mistake35° is only the angle of reflection; the question asks for the angle between the two rays.
39Multiple choice
On a diagram of a curved mirror, what name is given to the line drawn from the pole P through C, the centre of the sphere the mirror is cut from?
1. APrincipal axis
2. BAperture line
3. CFocal plane
4. DNormal to the pole
Show answer
Answer: A. Principal axis
The principal axis joins the pole P and the centre of curvature C.
Common mistake'Normal' is tempting because the axis is the normal at the pole, but its name is the principal axis.
40Multiple choice · ★ Challenge
For a concave mirror, a graph of uv (y-axis) against u + v (x-axis) is a straight line through the origin. Its gradient is equal to:
1. Ar
2. Bf
3. C2f
4. D1/f
Show answer
Answer: B. f
From 1/f = 1/u + 1/v = (u + v)/uv, we get uv = f(u + v), so the gradient is f.
Common mistake1/f is the gradient-like quantity in the 1/u, 1/v form; with uv against u + v the gradient is f itself.
41Multiple choice
In a ray diagram for a concave mirror, a ray from the top of the object is drawn so that it crosses F on its way to the mirror. How should the reflected ray be drawn?
1. AParallel to the principal axis
2. BBack along its own path to the object
3. CThrough the centre of curvature C
4. DBack through the principal focus again
Show answer
Answer: A. Parallel to the principal axis
Light paths are reversible: parallel rays reflect through F, so a ray through F reflects parallel to the axis.
Common mistake'Returns along its own path' is the rule for a ray through C, not through F.
42Multiple choice · ★ Challenge
A concave mirror forms a sharp image 4 times the size of an object on a screen 2.0 m from the mirror. How far is the object from the mirror?
1. A1.5 m
2. B0.4 m
3. C0.5 m
4. D8.0 m
Show answer
Answer: C. 0.5 m
m = v/u, so u = v/m = 2.0 ÷ 4 = 0.5 m (the focal length would be 0.4 m).
Common mistake8.0 m multiplies by the magnification; a magnified real image needs the object CLOSER than the image.
43Short answer · ★ Challenge
A learner records u and v for a concave mirror: u = 15 cm, v = 30.4 cm; u = 20 cm, v = 19.8 cm; u = 25 cm, v = 16.8 cm; u = 30 cm, v = 15.1 cm. Use f = uv/(u + v) to find f from each pair and give the mean.
Show answer
Model answer: f = 15 × 30.4 ÷ 45.4 ≈ 10.0 cm; 20 × 19.8 ÷ 39.8 ≈ 9.9 cm; 25 × 16.8 ÷ 41.8 ≈ 10.0 cm; 30 × 15.1 ÷ 45.1 ≈ 10.0 cm. Mean ≈ 10.0 cm.
Common mistakeAveraging the u and v values first and then calculating one f is less reliable; work out f for each pair, then average.
44Short answer
A torch has its bulb at the principal focus of a concave mirror; a solar cooker has its pot at the principal focus. Explain what is the same and what is different about the two.
Show answer
Model answer: Both use the principal focus of a concave mirror and both rely on the same ray rule: rays parallel to the axis pass through F, and rays from F reflect parallel (light paths are reversible). In the torch, light starts at F and leaves as a parallel beam. In the solar cooker, parallel rays from the Sun arrive and are concentrated at F, heating the pot.
Common mistakeSaying the two work by different rules is the error; it is the same rule with the light travelling in opposite directions.
45Short answer
The bowl of a spoon is part of a sphere of radius 6 cm. Which side acts as a concave mirror, and what are the focal lengths of the two sides?
Show answer
Model answer: The inside (hollow) of the bowl is concave, with f = r/2 = 3 cm. The back of the bowl is convex, with a focal length of 3 cm behind it (f = −3 cm in the real-is-positive convention).
Common mistakeSome give f = 12 cm by doubling; the focal length is HALF the radius.
46Short answer · ★ Challenge
Describe how to find, by a scale drawing, the image of an object 4 cm tall placed 28 cm from a concave mirror of focal length 12 cm. What should the drawing show?
Show answer
Model answer: Choose a scale, e.g. 1 cm : 5 cm. Draw the principal axis and the mirror; mark F at 12 cm (2.4 cm on paper) and C at 24 cm (4.8 cm). Draw the object 28 cm away (5.6 cm), 4 cm tall (0.8 cm). From its top draw a ray parallel to the axis that reflects through F, and a ray through F that reflects parallel to the axis. Where they cross is the top of the image. The drawing should show a real, inverted image about 21 cm from the mirror and about 3 cm tall (check: 1/v = 1/12 − 1/28 gives v = 21 cm, m = 0.75).
Common mistakeForgetting to scale both distances and heights the same way gives an image of the wrong size.
47Multiple choice
A rough way to find the focal length of a concave mirror is to form a sharp image of a distant window on a screen. The focal length is then:
1. AHalf the mirror-to-screen distance
2. BTwice the mirror-to-screen distance
3. CThe mirror-to-screen distance
4. DThe mirror-to-window distance
Show answer
Answer: C. The mirror-to-screen distance
Light from a very distant object arrives almost parallel, so its image forms at F: f = distance from mirror to screen.
Common mistake'Half the distance' confuses F with C; for a distant object the image is at F, not at C.
48Short answer · ★ Challenge
A pen 15 cm from an unknown mirror gives an upright image 10 cm behind the mirror. Find the focal length and state the type of mirror.
Show answer
Model answer: v = −10 cm (virtual). 1/f = 1/u + 1/v = 1/15 − 1/10 = −1/30, so f = −30 cm. A negative focal length means a convex mirror (consistent with an upright, diminished image).
Common mistakeUsing v = +10 cm gives f = +6 cm (a concave mirror), which contradicts the upright, smaller image.
49Multiple choice
A scale drawing uses 1 cm on paper to represent 5 cm. A concave mirror of focal length 15 cm is drawn with an object 40 cm away. How far from the mirror is F on the paper?
1. A3 cm
2. B75 cm
3. C8 cm
4. D15 cm
Show answer
Answer: A. 3 cm
15 cm ÷ 5 = 3 cm on paper.
Common mistake8 cm is the paper distance of the OBJECT (40 ÷ 5), not of the focus.
50Short answer · ★ Challenge
A shiny round Christmas bauble of diameter 8.0 cm acts as a convex mirror. A child's face 16 cm tall is 20 cm from it. Find the position and height of the image of the face.
Show answer
Model answer: r = 4.0 cm, so f = −2.0 cm. 1/v = 1/f − 1/u = −1/2.0 − 1/20 = −11/20, so v ≈ −1.8 cm (1.8 cm behind the surface, virtual). m = 1.8 ÷ 20 ≈ 0.091; image height = 0.091 × 16 ≈ 1.5 cm, upright.
Common mistakeUsing the diameter (8 cm) as the radius gives f = −4 cm and an image about twice too big.