Q. 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
A) $0.20\,\text{m}$
B) $0.25\,\text{m}$
C) $0.15\,\text{m}$
D) $0.10\,\text{m}$
Explanation
[Solution by Dr. Abubacker] Light refracts at the curved surface, reflects at the plane silvered face and refracts again. Power of the curved surface $=\frac{1.5-1.2}{R}=\frac{0.3}R$ (in liquid). The equivalent mirror has power $2\times\frac{0.3}R$, so $f=\frac{1.2}{0.6/R}=2R$. $2R=0.2\Rightarrow R=0.10$ m. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.