Optics Question 116
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, sees P and its image in the mirror. The apparent distance between these two will be
Options:
A) $ 2\mu \text{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 behind the mirror.
If d = depth of liquid in the tank.
Apparent depth of $ P=x _{1}=\frac{h}{\mu } $
Apparent depth of the image is given by $ 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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