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Question

Find the diameter of the image of the moon formed by a spherical concave mirror of focal length $$11.4 m. $$ The diameter of the moon is $$3450 km $$ and the distance between the earth and the moon is $$ 3.8 \times 10^5 km . $$


Solution

The diameter of the image of the moon can be calculated by using the below formula

$$m =  - \dfrac{v}{u}$$

Since we are given

$$u >  > f$$

Then we can replace $$v = f = 11.4m$$

By substituting all the values in the given equation we get

$$m =  - \dfrac{{11.4m}}{{3.8 \times {{10}^8}m}}$$

Also$$|m| = \dfrac{{{h_i}}}{{{h_f}}}$$

By equating and substituting the values we get the diameter of the moon as,

$$3 \times {10^{ - 8}} = \dfrac{{{h_i}}}{{3.45 \times {{10}^6}}}$$

$${h_i} = 10.35mm$$


Physics

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