Two spherical concave mirrors, each of focal length 20 cm are placed facing each other at a distance of 1 m such that their principal axes are parallel to each other and separated by distance 1 cm. Taking principal axis of mirror 2 along axis an object AB of length 1 cm is placed at origin as shown.
(i)Consider two successive reflections first from
mirror M-1 and then from mirror M-2, length of image formed will be –
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Ans.
(i)
Sol. For first reflection
f = –20, u = –60, ⇒ v = –30
m = 
= 
for second reflection
f = –20, u = –70 ⇒ v = – 28
m = – 
= – 0.4
m total = 
× (– 0.4) = 0.2
Length of image = 0.2 cm
(ii)
Sol. v = – 28
⇒ distance of image from mirror M-2 = 28 cm
(iii)
Sol. After first reflection image I 1 is inverted and of length 0.5 cm
After second reflection
y co-ordinate of A ′′ = (– 0.4) × 1.5 = – 0.6 cm
y co-ordinate of B ′′ = (– 0.4) × 1 = – 0.4 cm
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