JEE MAIN - Physics (2022 - 25th July Evening Shift - No. 24)
A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ____________ cm.
Answer
10
Explanation
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$${1 \over v} + {1 \over u} = {1 \over f}$$
$${1 \over v} - {1 \over { - 60}} = {1 \over {20}}$$
$${1 \over v} = - {1 \over {60}} + {1 \over {20}} = {{ - 1 + 3} \over {60}} = {2 \over {60}}$$
$$ \Rightarrow v = \, +\, 30$$ cm
$$\therefore$$ Radius of curvature of mirror = 30 $$-$$ 10 = 20 cm
$$ \Rightarrow {f_{mirror}} = {{20} \over 2} = 10$$ cm
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