Question 216 of 295

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

A0.20 mB0.25 mC0.15 mD0.10 m

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Answer: (D) 0.10 m

$\begin{aligned} & \frac{1.5}{\mathrm{v}}=\frac{1.5-1.2}{\mathrm{R}} \\ & \mathrm{v}=\frac{1.5 \mathrm{R}}{0.3}=5 \mathrm{R} \\ & \frac{1.2}{\mathrm{f}}-\frac{1.5}{5 \mathrm{R}}=\frac{1.2-1.5}{-\mathrm{R}} \\ & \frac{1.2}{\mathrm{f}}=\frac{0.3}{\mathrm{R}} \times 2 \Rightarrow \mathrm{f}=2 \mathrm{R} \Rightarrow \mathrm{R}=0.1\end{aligned}$