Question

For the given incident ray as shown in figure, the condition of total internal reflection of this ray the required refractive index of prism will be

• A. $\frac{\sqrt{3}+1}{2}$
• B. $\frac{\sqrt{2}+1}{2}$
• C. $\sqrt{\frac{3}{2}}$
• D. $\sqrt{\frac{7}{6}}$

Answer 1

Answer: (C)

from diagram

$\angle r+\angle \theta ={90}^0$

$\frac{\sin i}{\sin r}=\mu$

$\frac{\sin 45}{\sin r}=\mu$

$\sin r=\frac{1}{\mu \sqrt{2}}$

$\theta >c\sin \theta >\sin c$

$\sin (90-r)>\frac{1}{\mu }$

$\cos r>\frac{1}{\mu }$

$\sqrt{1-{\sin }^{2}r}>\frac{1}{\mu }$

$1-\frac{1}{2{\mu }^2}>\frac{1}{{\mu }^2}$

$1>\frac{1}{2}{\mu }^2+\frac{1}{{\mu }^2}$

${\mu }^2>\frac{3}{2}$

$\mu =\frac{\sqrt{3}}{\sqrt{2}}$