Question

In the diagram shown, a light ray is incident on the lower medium boundary at an angle ${45}^{\circ }$ with the normal. Light ray become tangential to the top part of medium$-2$ after all kind of refraction for ${\mu }_2>\sqrt{2}$. Which of the following statements is/are true?

• A. If ${\mu }_2>\sqrt{2}$ then angle of deviation is ${45}^{\circ }$.
  
• B. If ${\mu }_2<\sqrt{2}$ then angle of deviation is ${90}^{\circ }$.
• C. If ${\mu }_2<\sqrt{2}$ then angle of deviation is ${135}^{\circ }$.
• D. If ${\mu }_2>\sqrt{2}$ then angle of deviation is $0^{\circ }$.

Answer 1

Answer: (A), (B)

If ${\mu }_2<\sqrt{2}$ then angle of deviation is ${90}^{\circ }$.


Critical angle is given by
${\theta }_c={\sin }^{-1}\left(\frac{{\mu }_2}{{\mu }_1}\right)={\sin }^{-1}\left(\frac{{\mu }_2}{2}\right)$

If ${\mu }_2<\sqrt{2}$, then total internal reflection takes place and that ray reflects back, the angle of deviation is
${180}^{\circ }-({45}^{\circ }+{45}^{\circ })={90}^{\circ }$

If $\mu =\sqrt{2}$, then the ray passes tangentially at the first medium, the angle of deviation is ${180}^{\circ }-({45}^{\circ }+{90}^{\circ })={45}^{\circ }$

If $\mu >\sqrt{2}$, then the ray enters the second medium and, grazes the interface of medium$-2\&3$ as shown in figure.

So, the angle of refraction is ${90}^{\circ }$ in medium $3$.

The deviation is ${180}^{\circ }-({45}^{\circ }+{90}^{\circ })={45}^{\circ }$.