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Q.

A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an inverted image of the object coincident with it

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a

12 cm

b

30 cm

c

50 cm

d

60 cm

answer is C.

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Detailed Solution

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For lens $u = 30 c m, f = 20 c m,$ hence by using
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \Rightarrow \frac{1}{+ 20} = \frac{1}{v} - \frac{1}{- 30} \Rightarrow v = 60 c m$
The final image will coincide the object, if light ray falls normally on convex mirror as shown. From figure, it could be seen clearly that separation between lens and mirror is 60 – 10 = 50 cm.

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