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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Physics
Chapter
Ray Optics

JIPMER 2015 · Physics · Ray Optics

A vessel of depth t is half filled with a liquid having refractive...

A vessel of depth tt is half filled with a liquid having refractive index n1n_1 and the other half is filled with water of having refractive index n2n_2. The apparent depth of the vessel as viewed from top is

Options

  1. A2t(n1+n2)n1n2\frac{2 t\left(n_1+n_2\right)}{n_1 n_2}
  2. B\frac{t n_1 n_2}{\left(n_1+n_2\right)}
  3. Ct(n1+n2)2n1n2\frac{t\left(n_1+n_2\right)}{2 n_1 n_2}
  4. Dn1n2(n1+n2)t\frac{n_1 n_2}{\left(n_1+n_2\right) t}

Correct answer

C. t(n1+n2)2n1n2\frac{t\left(n_1+n_2\right)}{2 n_1 n_2}

Step-by-step solution

The apparent depth is given by I′=t1n1+t2n2=t/2n1+t/2n2=t(n1+n2)2n1n2\begin{aligned} I^{\prime} & =\frac{t_1}{n_1}+\frac{t_2}{n_2} \\ & =\frac{t / 2}{n_1}+\frac{t / 2}{n_2}=\frac{t\left(n_1+n_2\right)}{2 n_1 n_2}\end{aligned}
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