A light ray is incident on a mirror and gets reflected by it (Fig. 10.21). The angle made by the incident ray with the normal to the mirror is 40°. What is the angle made by the reflected ray with the mirror? (i) 40° (ii) 50° (iii) 45° (iv) 60°
Answer
(ii) 50°
Angle of incidence, i = 40° (measured from the normal) By the first law of reflection, r = i = 40° The normal is at 90° to the mirror, so angle with the mirror = 90° − r = 90° − 40° = 50°
Both i and r are measured from the normal, never from the mirror. If i = 40°, then r = 40°, and the angle between the reflected ray and the mirror surface is 90° − 40° = 50°.
Why 40° is the trap: the question gives the angle from the normal but asks for the angle from the mirror. The law i = r is about the normal only. Once r = 40° is found, the remaining step is simple geometry — the normal and the mirror are perpendicular, so the two angles at the point of incidence on that side must add up to 90°.
Tip: before answering any reflection question, underline whether the angle mentioned is measured from the normal or from the mirror. Almost every mistake in this topic starts there.
Q2.
Fig. 10.22 shows three different situations where a light ray falls on a mirror: (i) The light ray falls along the normal. (ii) The mirror is tilted, but the light ray still falls along the normal to the tilted surface. (iii) The mirror is tilted, and the light ray falls at an angle of 20° from the normal. Draw the reflected ray in each case (Use a ruler and protractor for accurate drawing). What is the angle of reflection in each case?
Answer
Draw the normal first in every case — at 90° to the mirror surface at the point where the ray strikes it. Then measure i from that normal and set r equal to it on the other side.
The reflected ray in each case. In (i) and (ii) the ray arrives along the normal, so i = 0° and the ray simply returns along its own path. In (iii) the reflected ray lies on the other side of the normal, also at 20°.
Case
Angle of incidence (i)
Angle of reflection (r)
Path of the reflected ray
(i)
0°
0°
Straight back along the incident ray
(ii)
0°
0°
Straight back along the incident ray
(iii)
20°
20°
At 20° on the other side of the normal (40° away from the incident ray)
Why (i) and (ii) give the same answer even though the mirrors are differently placed: tilting the mirror tilts its normal by the same amount. In (ii) the ray has been tilted along with the mirror, so the ray is still along the normal and i is still 0°. What decides the answer is not how the mirror is placed in the room but the angle between the ray and the normal — and that is unchanged.
Check it yourself: in (iii) the incident and reflected rays are 40° apart, that is 2 × 20°. This is always true — the angle between the incident and the reflected ray is twice the angle of incidence.
Q3.
In Fig. 10.23, the cap of a sketch pen is placed in front of three types of mirrors. Match each image with the correct mirror.
Answer
Compare each image in the mirror with the actual cap standing beside it.
Image
What it looks like
Mirror
(i)
Erect, but much smaller than the cap
Convex mirror
(ii)
Erect, and much larger than the cap
Concave mirror
(iii)
Erect, and the same size as the cap
Plane mirror
Why size alone settles it here: the cap is close to each mirror, and at close range the three mirrors are easy to separate. A plane mirror can only ever give a same-size image. A convex mirror can only ever give a diminished one. A concave mirror, with the object this close, gives an enlarged one. Since all three images are erect, orientation gives no clue — the size does.
Tip: if the cap in (ii) had been moved much farther back, the concave mirror would have shown it upside down. The concave mirror is the only one of the three that can do that.
Q4.
In Fig. 10.24, the cap of a sketch pen is placed behind a convex lens, a concave lens, and a flat transparent glass piece — all at the same distance. Match each image with the correct type of lens or glass.
Answer
All three pictures are taken at the same object distance, so any difference in size is caused by the glass alone.
Image
What it looks like
Lens/glass type
(i)
Erect and much enlarged, seen through a round lens
Convex lens
(ii)
Erect and much smaller, seen through a round lens
Concave lens
(iii)
Unchanged in size, seen through a flat square plate
Flat transparent glass piece
Why the flat plate leaves the cap unchanged: its two faces are parallel, so every ray is bent one way entering the glass and bent back by the same amount leaving it. The ray carries on in its original direction, only shifted slightly sideways, so the cap is seen at its true size. The two lenses have curved, non-parallel faces, so the bends do not cancel — the convex lens converges the light and enlarges the cap at this distance, and the concave lens diverges it and shrinks the cap.
Q5.
When the light is incident along the normal on the mirror, which of the following statements is true: (i) Angle of incidence is 90° (ii) Angle of incidence is 0° (iii) Angle of reflection is 90° (iv) No reflection of light takes place in this case
Answer
(ii) Angle of incidence is 0°
The angle of incidence is the angle between the incident ray and the normal. Here the incident ray lies along the normal, so the angle between them is i = 0° and therefore r = i = 0°
The light is reflected straight back along its own path.
Why the other options fail: 90° would be the angle the ray makes with the mirror surface, not with the normal — options (i) and (iii) come from measuring against the wrong line. Option (iv) is simply wrong: the mirror reflects the light perfectly well; it just sends it back the way it came, so there is no separate reflected beam to see.
Q6.
Three mirrors — plane, concave and convex are placed in Fig. 10.25. On the basis of the images of the graph sheet formed in the mirrors, identify the mirrors and write their names above the mirrors.
Answer
Compare the squares seen in each mirror with the squares of the real graph sheet standing behind them.
Mirror in Fig. 10.25
What the reflected graph sheet looks like
Mirror
Left
Squares are bigger than on the real sheet, so fewer of them fit in the mirror
Concave mirror
Middle
Squares are the same size as on the real sheet and the lines stay straight
Plane mirror
Right
Squares are smaller, many more of them fit in, and the lines are visibly bowed
Convex mirror
Why a graph sheet is such a good test object: a plain object only tells you its overall size. A grid tells you what the mirror does at every point at once — if the squares near the edge are a different size from those at the centre, the mirror must be curved, and the bending of the straight grid lines shows which way. In the middle mirror the grid is reproduced exactly, which no curved mirror can do; on the right the grid is both shrunk and bowed, the signature of a surface curving outwards.
Check it yourself: the convex mirror also shows a wider strip of the graph sheet than the other two. Squeezing a wider view into the same disc is exactly why the squares in it look small.
Q7.
In a museum, a woman walks towards a large concave mirror (Fig. 10.26). She will see that: (i) her erect image keeps decreasing in size. (ii) her inverted image keeps decreasing in size. (iii) her inverted image keeps increasing in size and eventually it becomes erect and magnified. (iv) her erect image keeps increasing in size.
Answer
(iii) her inverted image keeps increasing in size and eventually it becomes erect and magnified.
Follow the walk from a long way off:
Far from the mirror — the image is inverted and small, exactly as in Fig. 10.26 where she is shown upside down in the mirror.
Walking closer — the image stays inverted but grows larger.
Very close to the mirror — the image turns over and becomes erect and magnified.
Concave mirror with the object between F and the mirror. The two reflected rays spread apart, so they never meet in front of the mirror; extended backwards (dashed) they meet behind it. The image is therefore virtual — it cannot be caught on a screen — and it is erect and enlarged.
Why the flip happens on the way in: a concave mirror converges the reflected rays. While she is far away, those rays cross in front of the mirror before reaching her eye, and light that has crossed shows her upside down. As she comes nearer, the rays leaving her are spreading more steeply, and past a certain distance the mirror can no longer bring them to a crossing at all — they still diverge on the way to her eye, which traces them back to a point behind the mirror. That backward-traced image is erect and larger than her, and because no light actually arrives from behind the mirror it cannot be caught on a screen; such an image is called a virtual image.
Tip: options (i) and (iv) can be ruled out immediately — an image that stays erect the whole time is what a plane or a convex mirror gives, not a concave one.
Q8.
Hold a magnifying glass over text and identify the distance where you can see the text bigger than they are written. Now move it away from the text. What do you notice? Which type of lens is a magnifying glass?
Answer
A magnifying glass is a convex lens — a lens that is thicker at the middle than at its edges.
What you notice, step by step:
Held close to the page, the letters look erect and enlarged; there is a range of a few centimetres over which the print is both big and sharp.
As the lens is lifted, the letters get bigger still, up to a point.
At one particular height the print blurs completely and cannot be read.
Lift it further and the print reappears upside down and now gets smaller the higher you go.
Why the letters flip: a convex lens converges the light from the page. While the page is nearer than a certain distance the rays are still diverging when they reach your eye, so the eye traces them back to an enlarged, erect image. Beyond that distance the rays converge and cross before reaching your eye, and crossed rays give an inverted view. The blurred position in between is where the rays are neither properly diverging nor properly crossed.
Check it yourself: hold the magnifying glass at arm's length and look at a distant window through it. You will see the window upside down and tiny — which is the last step of the list above.
Q9.
Match the entries in Column I with those in Column II. Column I: (i) Concave mirror (ii) Convex mirror (iii) Convex lens (iv) Concave lens. Column II: (a) Spherical mirror with a reflecting surface that curves inwards. (b) It forms an image which is always erect and diminished in size. (c) Object placed behind it may appear inverted at some distance. (d) Object placed behind it always appears diminished in size.
Answer
Column I
Column II
Why
(i) Concave mirror
(a)
By definition — its reflecting surface curves inwards
(ii) Convex mirror
(b)
Its reflected rays always diverge, so the image can only be erect and diminished
(iii) Convex lens
(c)
It converges light, so beyond a certain distance the rays cross and the object appears inverted
(iv) Concave lens
(d)
It diverges light, so the object seen through it is always erect and diminished
How to be sure of (b) and (d): both entries say 'always', and only diverging optics can promise 'always'. Entry (b) says forms an image — the language of a mirror — so it must be the convex mirror. Entry (d) says object placed behind it — the language used for lenses in this chapter, since we look through a lens — so it must be the concave lens.
Q10.
The following question is based on Assertion/Reason. Assertion: Convex mirrors are preferred for observing the traffic behind us. Reason: Convex mirrors provide a significantly larger view area than plane mirrors. Choose the correct option: (i) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion. (ii) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion. (iii) Assertion is correct but Reason is incorrect. (iv) Both Assertion and Reason are incorrect.
Answer
(i) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Assertion — correct. Side-view mirrors on vehicles are convex mirrors.
Reason — correct. Because a convex mirror curves outwards, it collects light from a much wider strip of the road behind and shows it in the same small mirror.
And the Reason really is the explanation. A driver needs to see as much as possible of the road behind before changing lanes, and the widest view in the smallest mirror is precisely what a convex mirror gives. That is why it is chosen over a plane mirror of the same size.
The price paid for the wide view: squeezing a wider scene into the same mirror makes every vehicle look smaller, and a smaller image reads as a more distant one. This is exactly the reason the warning 'Objects in mirror are closer than they appear' is printed on the mirror. It is a drawback of the same property, not a different property — so it does not weaken the Reason.
Q11.
In Fig. 10.27, note that O stands for object, M for mirror, and I for image. Which of the following statements is true? (i) Figure (a) indicates a plane mirror and Figure (b) indicates a concave mirror. (ii) Figure (a) indicates a convex mirror and Figure (b) indicates a concave mirror. (iii) Figure (a) indicates a concave mirror and Figure (b) indicates a convex mirror. (iv) Figure (a) indicates a plane mirror and Figure (b) indicates a convex mirror.
Answer
(ii) Figure (a) indicates a convex mirror and Figure (b) indicates a concave mirror.
Compare the arrow marked I with the arrow marked O in each figure. In both figures the image is erect and lies on the far side of the mirror M, so only the size can tell them apart.
Figure
Image compared with object
Which mirror can do this
(a)
Erect and smaller than O
Convex mirror — its image is always erect and diminished
(b)
Erect and larger than O
Concave mirror, with the object close to it
Convex mirror. The reflected rays always diverge, so the image is found by extending them backwards. It is virtual — it cannot be caught on a screen — and it is erect and diminished; it always lies between the mirror and F — closer to the mirror than the object, however far away the object is taken.
Why a plane mirror is ruled out in both: a plane mirror gives an image exactly equal in size to the object, and in neither figure is I the same height as O. So options (i) and (iv), which both call one of the figures a plane mirror, cannot be right. Option (iii) has the two the wrong way round — enlargement is the concave mirror's doing, not the convex mirror's.
Tip: in both figures I is drawn on the opposite side of M from O — that is, behind the mirror. Both are therefore erect images traced back behind the mirror, which is the only kind a convex mirror ever makes and the kind a concave mirror makes when the object is close.
Q12.
Place a pencil behind a transparent glass tumbler (Fig. 10.28a). Now fill the tumbler halfway with water (Fig. 10.28b). How does the pencil appear when viewed through the water? Explain why its shape appears changed.
Answer
Through the empty tumbler the pencil looks normal. Once the tumbler is half filled, the part of the pencil seen through the water looks distinctly broader than the part above the water level, and it is shifted a little to one side — so the pencil seems to break at the water surface.
Through the empty tumbler the pencil looks normal. Through the water the lower part looks broader and shifted sideways, so the pencil seems to break at the water surface.
Why the shape appears changed: the tumbler filled with water is a transparent body with a curved outer surface — a cylindrical convex lens lying on its side. Light coming from the pencil bends as it passes from water and glass into air. Because the surface is curved, rays leaving from the left and the right edges of the pencil are bent inwards by different amounts, so they reach your eye more widely separated than they started. Your eye traces them back in straight lines and places the pencil wider than it really is. Above the water line there is only air and a thin curved sheet of glass, which bends the light hardly at all — so that part is seen at its true width, and the two parts no longer line up.
Try This: a curved surface only magnifies across the curve. Turn the tumbler in your hand and the pencil widens sideways but never gets taller — because the tumbler is curved only around its sides, not up and down.