Question

In the diagram shown , a light ray is incident on the lower medium boundary at an angle ${45}^o$ with the normal

• A. If ${\mu }_2<\sqrt{2}$ then deviation suffered by the light ray is ${90}^o$
• B. If ${\mu }_2>\sqrt{2}$ then total deviation suffered by the light ray is ${45}^o$
• C. If ${\mu }_2>\sqrt{2}$ then total deviation suffered by light ray is ${90}^o$
• D. If ${\mu }_2>\sqrt{2}$ then total deviation suffered by light ray is ${45}^o$

Answer 1

Answer: (A)

If ${\mu }_2<\sqrt{2}$ then deviation suffered by the light ray is ${90}^o$

For ${\mu }_2⟩\sqrt{2}$ (TIR will not take place) - (1)

$\begin{array}{cc}\frac{\sin 45}{\sin \gamma }& =\frac{{\mu }_2}{2}\\ \Rightarrow {\mu }_2& =\frac{x\sqrt{2}}{\sqrt{2}\sin \gamma }\end{array}$

$\Rightarrow \frac{\sqrt{2}}{\sin \gamma }>\sqrt{2}\text{( using-1)}$

$\Rightarrow \sin \gamma <1$

$\gamma <{90}^{\circ }$

So, deviation is approx ${45}^{\circ }$

If ${\mu }_2<\sqrt{2}$, TIR will take,

Then deviation must be ${90}^{\circ }$ or more