Optics Question 116

Question: A plane mirror is placed at the bottom of the tank containing a liquid of refractive index $ \mu $ . P is a small object at a height h above the mirror. An observer O-vertically above P outside the liquid see P and its image in the mirror. The apparent distance between these two will be

Options:

A) $ 2\mu h $

B) $ \frac{2h}{\mu } $

C) $ \frac{2h}{\mu -1} $

D) $ h( 1+\frac{1}{\mu } ) $

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Answer:

Correct Answer: B

Solution:

Image formation by a mirror (either plane or spherical) does not depend on the medium. The image of P will be formed at a distance h below the mirror.

If d = depth of liquid in the tank.

Apparent depth of $ P=x _{1}=\frac{d-h}{\mu } $

Apparent depth of the image of $ P=x _{2}=\frac{d+h}{\mu } $

Apparent distance between P and it’s image $ =x _{2}-x _{1}=\frac{2h}{\mu } $



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