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Question

A concave mirror has a radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to :
(Refractive index of water=1.33)


A
11.7 cm
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B
8.8 cm
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C
13.4 cm
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D
6.7 cm
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Solution

The correct option is B 8.8 cm
Given that, R=40 cmf=20 cm

If v is the distance of the image formed by the mirror, then, using mirror formula,

1v+1u=1f

1v+15=120

v=203 cm

Distance of this image from water surface

D=203+5=353 cm

Viewing from above the glass, Apparent depth due to refraction is given by,

d=Dμ

d=(353)1.33=8.8 cm

Hence, option (C) is correct.

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