Question

Find the diameter of the image of the moon formed by a spherical concave mirror of focal length $11.4m.$ The diameter of the moon is $3450km$ and the distance between the earth and the moon is $3.8\times {10}^{5}km.$

Answer 1

The diameter of the image of the moon can be calculated by using the below formula

$m=-\frac{v}{u}$

Since we are given

$u>>f$

Then we can replace $v=f=11.4m$

By substituting all the values in the given equation we get

$m=-\frac{11.4m}{3.8\times {10}^{8}m}$

Also$|m|=\frac{h_i}{h_f}$

By equating and substituting the values we get the diameter of the moon as,

$3\times {10}^{-8}=\frac{h_i}{3.45\times {10}^6}$

$h_i=10.35mm$