Q. A plano-convex lens having radius of curvature of first surface $2$ cm exhibits focal length of $f_1$ in air. Another plano-convex lens with first surface radius of curvature $3$ cm has focal length of $f_2$ when it is immersed in a liquid of refractive index $1.2$. If both the lenses are made of same glass of refractive index $1.5$, the ratio of $f_1$ and $f_2$ will be
A) $1:2$
B) $1:3$
C) $3:5$
D) $2:3$
Explanation
[Solution by Dr. Abubacker] In air: $\frac1{f_1}=\frac{0.5}2\Rightarrow f_1=4$ cm. In liquid: $\frac1{f_2}=\left(\frac{1.5}{1.2}-1\right)\frac13=\frac{0.25}3\Rightarrow f_2=12$ cm. $f_1:f_2=1:3$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.