Question

What will be 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 $3.8\times {10}^5$ km.

• A. 0.49 mm
• B. 0.59 mm
• C. 0.69 mm
• D. 0.79 mm

Answer 1

The correct option is C

0.69 mm

$u=-3.8\times {10}^5$km
using mirror formula $\frac{1}{v}+\frac{1}{v}=\frac{1}{f}$
$u=\infty$ so neglecting $\frac{1}{u}$
so $\frac{1}{v}=\frac{1}{f}\Rightarrow V=-7.6cm$
$m=-\frac{v}{u}=\frac{Heightofimage}{Heightofobject}\Rightarrow \frac{-(-7.6\times {10}^{-2})}{-3.8\times {10}^3}=\frac{H_1}{3450\times {10}^3}\Rightarrow \frac{-(7.6\times {10}^{-2}\times 3450\times {10}^3\times {10}^{-3})}{3.8}{H}_1\Rightarrow 2\times 3450\times {10}^{-7}\Rightarrow 69\times {10}^{-5}m\Rightarrow 69\times {10}^{-3}cm\Rightarrow 69\times {10}^{-2}cm\Rightarrow 0.69mm$