First slide

Ray optics

Question

The plane surface of a plano convex lens having radius of curvature 20 cm is silvered. If this silvered lens is equivalent to a concave mirror, the radius of curvature of the mirror is (Refractive index of glass is 1.5)

Difficult

A

80 cm
B

30 cm
C

40 cm
D

60 cm

Solution

Focal length of a silvered lens is given by
$\frac{1}{F} = - \frac{2}{f_{l}} + \frac{1}{f_{m}}$
The silvered surface behaves like a plane mirror, therefore $f_{m} = \infty$ . Also $\frac{1}{f_{l}} = \frac{μ - 1}{R} = \frac{1 .5 - 1}{20} = \frac{1}{40}$
$∴ \frac{1}{F} = - 2 \times \frac{1}{40} \Rightarrow F = - 20 cm$
So focal length of the concave mirror is 20 cm. Hence radius of curvature $= 2 \times 20 cm = 40 cm$

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