Question

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

• A. $7cm$
• B. $6cm$
• C. $8cm$
• D. $9cm$

Answer 1

Answer: (A)

$7cm$

Given, $f=-7.6m$

$h_o=3450km=3450\times {10}^{3}m$

$u=3.8\times {10}^{5}km=3.8\times {10}^{8}m$

Hence compared to the focal length the object distance is infinite.

$\therefore \frac{1}{f}=\frac{1}{v}+\frac{1}{u}=\frac{1}{v}+\frac{1}{\infty }=\frac{1}{v}$

$\Rightarrow f=v=-7.6m$

Magnification, $m=\frac{h_i}{h_o}=-\frac{v}{u}$

$\Rightarrow h_i=-h_o\frac{v}{u}$

$\Rightarrow h_i=3450\times {10}^3\times \frac{7.6}{3.8\times {10}^8}=0.069m=6.9cm$

Hence, the approximate diameter of the image of the moon is $7cm$,

Hence the correct answer is option (A).