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A plano-convex lens ($\mu$ = 1.5) has radius of curvature 10 cm. It is silvered on its plane surface. Find focal length after silvering :
A
10 cm
B
20 cm
C
15 cm
D
25 cm
Detailed Solution
When one surface of a lens is silvered, it behaves as a mirror. Light passes through the lens, reflects from the silvered surface, and passes through the lens again.
Equivalent power: $P_{eq} = 2P_L + P_M$
Power of the plano-convex lens: $P_L = (\mu - 1)\dfrac{1}{R}$; the silvered plane surface is a plane mirror with $P_M = 0$.
$P_{eq} = 2(\mu - 1)\dfrac{1}{R} + 0$
$f = -\dfrac{1}{P_{eq}} = -\dfrac{R}{2(\mu - 1)} = -\dfrac{10}{2(1.5 - 1)} = -10$ cm
So it acts as a concave mirror of focal length 10 cm.
Equivalent power: $P_{eq} = 2P_L + P_M$
Power of the plano-convex lens: $P_L = (\mu - 1)\dfrac{1}{R}$; the silvered plane surface is a plane mirror with $P_M = 0$.
$P_{eq} = 2(\mu - 1)\dfrac{1}{R} + 0$
$f = -\dfrac{1}{P_{eq}} = -\dfrac{R}{2(\mu - 1)} = -\dfrac{10}{2(1.5 - 1)} = -10$ cm
So it acts as a concave mirror of focal length 10 cm.