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} $
Show Answer
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}}} ) $
