Find the diameter of the image of the moon formed by a spherical concave mirror of focal length 7.6m. The diameter of the moon is 3450km and the distance between the earth and the moon is $3.8 \times 10^5km.$
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$u = -3.8 \times 10^5km$
diameter of moon $= 3450km ; f = -7.6m$
$\therefore \ \frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}\Rightarrow\frac{1}{\text{v}}+\Big(-\frac{1}{3.8\times10^5}\Big)=\Big(-\frac{1}{7.6}\Big)$
Since, distance of moon from earth is very large as compared to focal length it can be taken as $\infty.$
⇒ Image will be formed at focus, which is inverted.
$\Rightarrow\frac{1}{\text{v}}=-\Big(\frac{1}{7.6}\Big)\Rightarrow\text{v}=-7.6\text{m}$
$\text{m}=-\frac{\text{v}}{\text{u}}=\frac{\text{d}_{\text{image}}}{\text{d}_{\text{object}}}\Rightarrow\frac{-(-7.6)}{(-3.8\times10^8)}=\frac{\text{d}_{\text{image}}}{3450\times10^3}$
$\text{d}_{\text{image}}=\frac{3450\times7.6\times10^3}{3.8\times10^8}=0.069\text{m}=6.9\text{cm}.$
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