Q137 / 170 · Manipal (MET) 2016 · Physics

A ray of light is travelling through a medium of refractive index $\frac{1}{\sqrt{2}}$ with respect to air. When it is incident on the surface making an angle $45^{\circ}$ with the surface, which of the following will take place?

  • A
    Angle of refraction will be $45^{\circ}$
  • Correct answer
    B
    Angle of refraction will be $90^{\circ}$
  • C
    The ray will be internally reflected
  • D
    None of the above

Solution

Given, $\mu=\frac{1}{\sqrt{2}}$ w.r.t. air $i=45^{\circ}, r=$ ? Also, $\mu=\frac{\sin i}{\sin r}$ $\Rightarrow \quad \frac{1}{\sqrt{2}}=\frac{\sin 45^{\circ}}{\sin r} \Rightarrow \frac{1}{\sqrt{2}}=\frac{1 / \sqrt{2}}{\sin r}$ $\begin{aligned} \Rightarrow & & \sin r & =1 \\ \Rightarrow & & r & =90^{\circ}\end{aligned}$ Note that the ray is incident from denser medium and is refracted into a rarer medium air.

Hence, the correct answer is option: 'B'.

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