A thin plano-convex lens acts like a concave mirror of focal length $0.2$ m when silvered from its plane surface. The refractive index of the material of the lens is $1.5$ . The radius of curvature of the convex surface of the lens will be :

0.1

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0.75

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0.4

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0.2

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Solution

The correct option is D $0.2$ m
After silvering the plane surface, plano-convex lens behaves as a concave mirror of focal length
$\frac{1}{F} = \frac{2}{f_{l e n s}}$
But $F = 0.2$ m
$∴ f_{l e n s} = 2 F = 2 \times 0.2 = 0.4$ m
Now, from lens marker's formula
$\frac{1}{f_{l e n s}} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$
$∴ \frac{1}{0.4} = (1.5 - 1) \times \frac{1}{R_{1}}$ $[∵ R_{2} = \infty]$
$\Rightarrow R_{1} = 0.5 \times 0.4 = 0.2$ m.

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A thin plano-convex lens acts like a concave mirror of focal length 0.2m when silvered from its plane surface. The refractive index of the material of the lens is 1.5. The radius of curvature of the convex surface of the lens will be :

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A thin plano-convex lens acts like a concave mirror of focal length $0.2$ m when silvered from its plane surface. The refractive index of the material of the lens is $1.5$ . The radius of curvature of the convex surface of the lens will be :