Question

A cube of side length $1mm$ is placed on the axis of a concave mirror at a distance of $45cm$ from the pole, as shown in the figure. One edge of the cube is parallel to the axis. The focal length of the mirror is $30cm$. Find the approximate volume of the image.

Answer 1

from mirror formula

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

$\frac{1}{v}-\frac{1}{45}=-\frac{1}{30}$

$v=-90$ cm

Transverse magnification is $\frac{dv}{du}=-(\frac{v}{u}{)}^2$

$dv=-\frac{{90}^2}{{45}^2}=-4$mm

londitudinal magnification is $\frac{h_i}{h_o}=-\frac{v}{u}$

$h_i=-\frac{90}{45}=-2$ mm

so volume=$4\times 2\times 1$=$8m{m}^3$