First slide

The lens

Question

A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm. When its curved surface is silvered and the plane surface not silvered, it is equivalent to a concave mirror of focal length 10cm, then the refractive index of the material of the lens is:

Moderate

A

$\frac{9}{14}$
B

$\frac{14}{9}$
C

$\frac{17}{9}$
D

None

Solution

When plane surface is silvered, we use
$P_{eq} = 2 P_{L} = 2 (\frac{μ - 1}{R})$
Then in case when curved surface is silvered, we use
$P_{eq} = 2 P_{L} + P_{m}$ ,
$\Rightarrow P_{eq} = 2 (\frac{μ - 1}{R}) + \frac{2}{R} = \frac{2 μ}{R}$
Given that, $f_{eq} = 28 cm$
So we use $28 = \frac{R}{2 (μ - 1)} .... (1)$
When curved surface is silvered, we use
$f_{eq} = \frac{R}{2 μ} = 10.... (2)$
From equation (1) and (2) we get,
$μ = \frac{14}{9}$

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