Question

Find the diameter of the image of the moon, formed by a spherical concave mirror of focal length $7.6m$. The diameter of the moon is $3450km$ and the distance between the earth and moon is $3.8\times {10}^{5}km$.

Answer 1

$u=-3.8\times {10}^{5}km$

diameter of moon $=3450km;f=-7.6m$

$\therefore \frac{1}{v}+\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}+(-\frac{1}{3.8\times {10}^5})=(-\frac{1}{7.6})$

Since, distance of moon from earth is very large as compared to focal length it can be taken as $\infty$

$\Rightarrow$ Image will be formed at focus, which is inverted.

$\Rightarrow \frac{1}{v}=-\left(\frac{1}{7.6}\right)\Rightarrow v=-7.6m$

$m=-\frac{v}{u}=\frac{d_{image}}{d_{object}}=\frac{-(-7.6)}{(-3.8\times {10}^8)}=\frac{d_{image}}{3450\times {10}^3}$

$d_{image}=\frac{3450\times 7.6\times {10}^3}{3.8\times {10}^8}=0.069m=6.9m$