A glass slab has the left half of refractive index $n_{1}$ , and the right half of $n_{2} = 3 n_{1}$ . The effective refractive index of the whole slab is

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$\frac{n_{1}}{2}$

$2 n_{1}$

$\frac{3 n_{1}}{2}$

$\frac{2 n_{1}}{3}$

answer is C.

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Detailed Solution

$\begin{array}{l} Applying apparent depth formula \\ \frac{d}{n_{e f f}} = \frac{\frac{d}{2}}{n_{1}} + \frac{\frac{d}{2}}{n_{2}} \\ \Rightarrow n_{e f f} = \frac{2 n_{1} n_{2}}{n_{1} + n_{2}} = \frac{3}{2} n_{1} \end{array}$

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