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 $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$ .
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Solution
To burn in minimum time distance of paper must be at focus.
So $\mathrm{f}=30 \mathrm{~cm}$
$$
\begin{aligned}
& \frac{1}{30}=(\mu-1)\left(\frac{1}{60}-\frac{1}{-60}\right) \\
& \frac{1}{30}=\frac{\mu-1}{30} \\
& \mu=2 \\
& \alpha=20
\end{aligned}
$$
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