Q 12-09-196JEE MainJEE Main 2019 (10 Apr, Shift 1)Medium
One plano-convex and one plano-concave lens of the same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is $\mu_1$ and that of 2 is $\mu_2$, then the focal length of the combination is:
Answer: (D) $\dfrac{R}{\mu_1-\mu_2}$
By the lens maker's formula with one plane face:
$$\frac1{f_1} = \frac{\mu_1-1}{R},\qquad \frac1{f_2} = -\frac{\mu_2-1}{R}$$
For lenses in contact:
$$\frac1f = \frac{\mu_1-1}{R} - \frac{\mu_2-1}{R} = \frac{\mu_1-\mu_2}{R} \;\Rightarrow\; f = \frac{R}{\mu_1-\mu_2}$$
Solution by Sreeraj P, M.Sc Physics