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

Question

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 (A) 0.1 m (B) 0.75 m (C) 0.4 m (D) 0.2 m

Tardigrade Admin · Accepted Answer

After silvering the plane surface, plano-convex lens behaves as a concave mirror of focal length

\frac{1}{F} = \frac{2}{f _{lens}}

But

F = 0.2 m

∴ f_{lens} = 2 F = 2 \times 0.2 = 0.4 m

Now, from lens maker's formula

\frac{1}{f _{lens}} = (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

Q. 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

0.1 m

0.75 m

0.4 m

0.2 m

Q. 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