A ray of light enters into a thick glass slab from air as shown in figure. The refractive index of the glass slab varies with the depth x form the top most surface of the slab as μ=(3−x3), where x is in meters. Slab is of sufficiently large thickness. The maximum depth reached by the ray inside the slab is n×10−1 metre. Then the value of n is

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A ray of light enters into a thick glass slab from air as shown in figure. The refractive index of the glass slab varies with the depth $x$ form the top most surface of the slab as $μ = (\sqrt{3} - \frac{x}{\sqrt{3}}),$ where $x$ is in meters. Slab is of sufficiently large thickness. The maximum depth reached by the ray inside the slab is $n \times 10^{- 1}$ metre. Then the value of $n$ is

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Detailed Solution

$\begin{array}{l} μ = \sqrt{3} - \frac{1}{\sqrt{3}} x \\ n_{1} s i n i = n_{2} s i n r \\ \Rightarrow 1 \times \frac{\sqrt{3}}{2} = \frac{(3 - x)}{\sqrt{3}} \sin (90^{0}) \\ ⇒ \frac{3}{2} = (3 - x) \\ \Rightarrow x = (3 - \frac{3}{2}) = 1.5 \end{array}$