Optics Question 759

Question: Each quarter of a vessel of depth H is filled with liquids of the refractive indices $ n _{1},n _{2},n _{3} $and $n _{4} $ from the bottom respectively. The apparent depth of the vessel when looked normally is

[AMU (Engg.) 2000]

Options:

A) $ \frac{H(n _{1}+n _{2}+n _{3}+n _{4})}{4} $

B) $ \frac{H( \frac{1}{n _{1}}+\frac{1}{n _{2}}+\frac{1}{n _{3}}+\frac{1}{n _{4}} )}{4} $

C) $ \frac{(n _{1}+n _{2}+n _{3}+n _{4})}{4H} $

D) $ \frac{H( \frac{1}{n _{1}}+\frac{1}{n _{2}}+\frac{1}{n _{3}}+\frac{1}{n _{4}} )}{2} $

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Answer:

Correct Answer: B

Solution:

Apparent depth of bottom = $ \frac{H/4}{{\mu _{1}}}+\frac{H/4}{{\mu _{2}}}+\frac{H/4}{{\mu _{3}}}+\frac{H/4}{{\mu _{4}}} $

$ =\frac{H}{4}( \frac{1}{{\mu _{1}}}+\frac{1}{{\mu _{2}}}+\frac{1}{{\mu _{3}}}+\frac{1}{{\mu _{4}}} ) $



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