First slide

Ray optics

Question

Light enters at an angle of incidence in a transparent rod, through one end. Refractive index of the material of the rod is $' μ'$ The light once entered into it will not leave it through its lateral face, whatsoever be the value of angle of incidence, if

Moderate

Solution

$\begin{array}{l} {sinθ}_{c} = \frac{1}{μ} \\ r = 90^{0} - θ_{c} \\ Now, \frac{\sin 90^{0}}{sinr} = μ \\ \Rightarrow \frac{1}{{cosθ}_{c}} = μ \Rightarrow \sqrt{1 - \frac{1}{μ^{2}}} = \frac{1}{μ} \Rightarrow μ = \sqrt{2} \end{array}$

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