Question

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

Answer 1

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

Diameter of moon = 3450 km

f = -7.6 m

$\Rightarrow \frac{1}{v}=\frac{1}{u}+\frac{1}{f}$

$\therefore \frac{1}{v}+(-\frac{1}{3.8\times {10}^5})=\left(\frac{1}{57.6}\right)$

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.

$\Rightarrow \frac{1}{v}=-\frac{1}{7.6}$

$\Rightarrow v=-7.6\text{m}$

$m=-\frac{v}{u}=\frac{d_{\text{image}}}{d_{\text{object}}}$

$\Rightarrow \frac{-(-7.6)}{(-3.8\times {10}^8)}=\frac{d_{\text{image}}}{3450\times {10}^3}$

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

$=0.069\text{m}=6.9\text{cm}$