Q 12-09-133JEE MainJEE Main 2022 (24 Jun, Shift 1)Medium
Two identical thin biconvex lenses of focal length $15\ \text{cm}$ and refractive index $1.5$ are in contact with each other. The space between the lenses is filled with a liquid of refractive index $1.25$. The focal length of the combination is ______ cm.
Numerical value type. Enter your answer.
Answer: 10
For each glass lens: $\dfrac1{15} = (1.5-1)\dfrac{2}{R}\Rightarrow R = 15\ \text{cm}$.
The liquid forms a biconcave lens with both radii $15\ \text{cm}$:
$$\frac1{f_l} = (1.25-1)\left(-\frac{2}{15}\right) = -\frac1{30}$$
$$\frac1F = \frac1{15} + \frac1{15} - \frac1{30} = \frac{3}{30}\ \Rightarrow\ F = 10\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics