Q. Given is a thin convex lens of glass (refractive index $\mu$) and each side having radius of curvature $R$. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?
A) $R/\mu$
B) $R/(2\mu-3)$
C) $\mu R$
D) $R/(2\mu-1)$
Explanation
[Solution by Dr. Abubacker] For a silvered lens $\frac1{f_{eq}}=\frac2{f_L}+\frac1{f_m}=\frac{4(\mu-1)}R+\frac2R=\frac{2(2\mu-1)}R$. The image falls on the object when the object is at the centre of curvature of the equivalent mirror, i.e. at $2f_{eq}=\frac R{2\mu-1}$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.