Question

A telescope made of mirrors is used to observe the moon. It forms the inverted image of the moon at 3.5 km from the eye piece. Find the diameter of the image of the moon. Given the diameter of the moon is 1700 km and the distance of the moon from the earth is 350,000 km.

• A. $h^{{}^{\prime }}=1700m$
• B. $h^{{}^{\prime }}=3.5m$
• C. $h^{{}^{\prime }}=17m$
• D. $h^{{}^{\prime }}=350,000m$

Answer 1

The correct option is C $h^{{}^{\prime }}=17m$

Given:
$h=$ diameter of moon $=1700km$
$u=350,00km$ distance of moon from the earth (object distance)
$v=3.5km$ distance of image of moon from the earth (image distance)
Let $h^{{}^{\prime }}$ be the image distance i.e., the diameter of the moon's image. and $M$ be the magnification.

We know that,
$M=\frac{h^{\prime }}{h}=-\frac{v}{u}$
On substituting the given values we get,
$\frac{h^{\prime }}{1700}$ = $-\frac{3.5}{350000}$
$h^{{}^{\prime }}=-17\times {10}^{-3}km=-17m$. The negative sign shows that the image of the moon is inverted.
Diameter of moon’s image$=17m$