Q129 / 180 · JIPMER 2015 · Physics

A vessel of depth $t$ is half filled with a liquid having refractive index $n_1$ and the other half is filled with water of having refractive index $n_2$. The apparent depth of the vessel as viewed from top is

  • A
    $\frac{2 t\left(n_1+n_2\right)}{n_1 n_2}$
  • B
    $\frac{t n_1 n_2}{\left(n_1+n_2\right)}$
  • Correct answer
    C
    $\frac{t\left(n_1+n_2\right)}{2 n_1 n_2}$
  • D
    $\frac{n_1 n_2}{\left(n_1+n_2\right) t}$

Solution

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

Hence, the correct answer is option: 'C'.

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