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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