Q 12-09-173JEE MainJEE Main 2021 (27 Aug, Shift 2)Medium
Curved surfaces of a plano-convex lens of refractive index $\mu_1$ and a plano-concave lens of refractive index $\mu_2$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses
Answer: (D) $\mu_1 - \mu_2$
Plano-convex lens: $\dfrac{1}{f_1} = \dfrac{\mu_1 - 1}{R}$. Plano-concave lens: $\dfrac{1}{f_2} = -\dfrac{\mu_2 - 1}{R}$.
In contact:
$$\frac{1}{f} = \frac{\mu_1 - 1}{R} - \frac{\mu_2 - 1}{R} = \frac{\mu_1 - \mu_2}{R} \Rightarrow \frac{R}{f} = \mu_1 - \mu_2$$
Solution by Sreeraj P, M.Sc Physics