First slide

Spherical refracting surface's

Question

A ray of light falls on transparent sphere with centre at C as shown in the figure. The ray emerges from the sphere parallel to the line AB. The refractive index of the sphere is $\sqrt{x}$ then x is

Moderate

Solution

$\begin{array}{l} E x t e r i o r a n g l e i s s u m o f o p p o s i t e i n t e r i o r a n g l e s \\ 60^{0} = r + r \\ \Rightarrow r = 30^{0} \\ A p p l y S n e l l' s L a w \\ ∴ μ = \frac{\sin 60^{0}}{\sin 30^{0}} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} \\ ∴ μ = \sqrt{3} \\ H e n c e, x = 3 \end{array}$

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