Johnathon Arnold

2023-03-08

Find 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 xx 10^5 km

loans911z2s

Beginner2023-03-09Added 1 answers

$u=-3.8\times {10}^{5}\text{}km$

Diameter of moon = 3450 km

$f=-7.6\text{}m\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{1}{v}=\frac{1}{u}+\frac{1}{f}\phantom{\rule{0ex}{0ex}}\therefore \frac{1}{v}+(-\frac{1}{3.8\times {10}^{5}})=(\frac{1}{57.6})$

Given that the moon is much farther away from Earth than the focal length, it can be assumed that $\mathrm{\infty}$

$\Rightarrow $ At the focus, an inverted image will be created.

$\Rightarrow \frac{1}{v}=-\frac{1}{7.6}\phantom{\rule{0ex}{0ex}}\Rightarrow v=-7.6\text{}m\phantom{\rule{0ex}{0ex}}m=-\frac{v}{u}=\frac{{d}_{image}}{{d}_{object}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{-(-7.6)}{(-3.8\times {10}^{8})}=\frac{{d}_{image}}{3450\times {10}^{3}}\phantom{\rule{0ex}{0ex}}{d}_{image}=\frac{3450\times 7.6\times {10}^{3}}{3.8\times {10}^{8}}\phantom{\rule{0ex}{0ex}}=0.069m=6.9\text{}cm$

Diameter of moon = 3450 km

$f=-7.6\text{}m\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{1}{v}=\frac{1}{u}+\frac{1}{f}\phantom{\rule{0ex}{0ex}}\therefore \frac{1}{v}+(-\frac{1}{3.8\times {10}^{5}})=(\frac{1}{57.6})$

Given that the moon is much farther away from Earth than the focal length, it can be assumed that $\mathrm{\infty}$

$\Rightarrow $ At the focus, an inverted image will be created.

$\Rightarrow \frac{1}{v}=-\frac{1}{7.6}\phantom{\rule{0ex}{0ex}}\Rightarrow v=-7.6\text{}m\phantom{\rule{0ex}{0ex}}m=-\frac{v}{u}=\frac{{d}_{image}}{{d}_{object}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{-(-7.6)}{(-3.8\times {10}^{8})}=\frac{{d}_{image}}{3450\times {10}^{3}}\phantom{\rule{0ex}{0ex}}{d}_{image}=\frac{3450\times 7.6\times {10}^{3}}{3.8\times {10}^{8}}\phantom{\rule{0ex}{0ex}}=0.069m=6.9\text{}cm$