A concave mirror of radius of curvature 60cm is placed at the bottom of a tank containing water up to a height of 20cm. The mirror faces upwards with its axis vertical. Sunlight falls normally on the surface of the water and the image of the sun is formed. If refractive index of water is $\frac{4}{3}$ then with the observer in air, the distance of the image from the surface of water is

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Solution

The focal length of the mirror:
$f = \frac{R}{2} = 30 c m$
As the water is filled up to the height of 20 cm light rays suffer refraction at the surface.
So, the real height is equal to the difference of focal length and height of water.
Real height = 30 - 20 = 10 cm
Determination of apparent depth:
$μ = \frac{104}{3} = 7.5 c m$
Hence, the distance of the image from the surface of water is equal to 7.5 cm.

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