A ray of light travelling in a transparent medium of refractive index $\mu$ falls, on a surface separating…

A ray of light travelling in a transparent medium of refractive index $\mu$ falls, on a surface separating the medium from air at an angle of incidence of $45^{\circ}$. For which of the following value of $\mu$ the ray can undergo total internal reflection?
  1. $\mu=1.33$
  2. $\mu=1.40$
  3. $\mu=1.50$
  4. $\mu=1.25$

Solution

For total internal reflection $\begin{aligned} & \mathrm{i} > \mathrm{c} \\ \Rightarrow & \sin \mathrm{i} > \sin \mathrm{c} \\ \Rightarrow & \sin 45^{\circ} > \frac{1}{\mu} \\ \Rightarrow & \mu > \sqrt{2} \\ \Rightarrow & \mu > 1.4 \end{aligned}$

Asked in: NEET 2010 (Screening)

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