Q 12-09-193JEE MainJEE Main 2019 (10 Jan, Shift 1)Medium
A plano-convex lens of refractive index $\mu_1$ and focal length $f_1$ is kept in contact with another plano-concave lens of refractive index $\mu_2$ and focal length $f_2$. If the radius of curvature of their spherical faces is $R$ each and $f_1 = 2f_2$, then $\mu_1$ and $\mu_2$ are related as:
Answer: (D) $2\mu_1 - \mu_2 = 1$
Lens maker's formula with one plane face gives focal lengths of magnitude
$$|f_1| = \frac{R}{\mu_1-1},\qquad |f_2| = \frac{R}{\mu_2-1}$$
Taking $f_1 = 2f_2$ in magnitude:
$$\frac{R}{\mu_1-1} = \frac{2R}{\mu_2-1} \;\Rightarrow\; \mu_2 - 1 = 2\mu_1 - 2 \;\Rightarrow\; 2\mu_1 - \mu_2 = 1$$
Solution by Sreeraj P, M.Sc Physics