Question

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is :-

(1) 0.15 m

(2) 0.10 m

(3) 0.20 m

(4) 0.25 m

Answer 1

Correct option is : (2) 0.10 m

\(\frac{1.5}{v} = \frac{1.5 - 1.2}{R}\) 

\( \mathrm{v}=\frac{1.5 \mathrm{R}}{0.3}=5 \mathrm{R}\) 

\(\frac{1.2}{\mathrm{f}}-\frac{1.5}{5 \mathrm{R}}=\frac{1.2-1.5}{-\mathrm{R}}\) 

\(\frac{1.2}{\mathrm{f}}=\frac{0.3}{\mathrm{R}} \times 2 \Rightarrow \mathrm{f}=2 \mathrm{R} \Rightarrow \mathrm{R}=0.1\)