Q 12-09-052JEE MainJEE Main 2026 (2 Apr, Shift 2)Easy
If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at $30$ cm above the paper. If the radius of curvature of the lens is $60$ cm then the refractive index of the lens material is $\dfrac{\alpha}{10}$. The value of $\alpha$ is ______.
Numerical value type. Enter your answer.
Answer: 20
The paper burns fastest when it is at the focus, so $f=30$ cm.
For an equiconvex lens with both radii $60$ cm (lens maker's formula):
$$\frac1f=(\mu-1)\left(\frac1{60}+\frac1{60}\right)\ \Rightarrow\ \frac1{30}=\frac{\mu-1}{30}\ \Rightarrow\ \mu=2$$
$\mu=\dfrac{20}{10}$, so $\alpha=20$.
Solution by Sreeraj P, M.Sc Physics