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(B) The shortest time to burn the paper occurs when the sunlight is focused exactly at the focal point of the lens. Therefore, the focal length $f = 3

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) The shortest time to burn the paper occurs when the sunlight is focused exactly at the focal point of the lens. Therefore, the focal length $f = 30 	ext{ cm}$.Using the lens maker's formula: $\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} ight)$.For a symmetric double convex lens, $R_1 = R = 60 	ext{ cm}$ and $R_2 = -R = -60 	ext{ cm}$.Substituting these values: $\frac{1}{30} = (\mu - 1) \left( \frac{1}{60} - \frac{1}{-60} ight)$.$\frac{1}{30} = (\mu - 1) \left( \frac{1}{60} + \frac{1}{60} ight) = (\mu - 1) \left( \frac{2}{60} ight) = (\mu - 1) \left( \frac{1}{30} ight)$.This implies $\mu - 1 = 1$, so $\mu = 2$.Given $\mu = \frac{\alpha}{10}$, we have $2 = \frac{\alpha}{10}$, which gives $\alpha = 20$.

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