Question

The refractive index of the material of an equilateral prism is 1.5. If a ray of light is incident at an angle ${15}^0$ on one side, then

• A. angle of emergence is ${60}^0$
• B. angle of deviation is ${90}^0$
• C. angle of deviation is ${30}^0$
• D. the ray will not emerge out of second

Answer 1

The correct option is A angle of emergence is ${60}^0$

$\begin{array}{c}\text{applying enell's law}\\ \sin {75}^{\circ }={\mu }_1\sin {\Omega }_1\\ \frac{\sqrt{3}+1}{2\sqrt{2}}=\frac{3}{2}\mathrm{lin}{\Omega }_1\\ \mathrm{lin}{r}_1=\frac{\sqrt{3}+1}{3\sqrt{2}}\end{array}$

$\text{sinr\_(1)}=\frac{2.73}{4.24}=0.643$

$\begin{array}{cc}{n}_1& =Si{n}^{-1}\left(0.643\right)\\ n_1& ={25.76}^{\circ }\simeq {25.8}^{\circ }\end{array}$

$\begin{array}{cc}{r}_1+r_2& ={60}^{\circ }\\ r_2& ={34.2}^{\circ }\end{array}$

usingn = eine

$\frac{3}{2}\times \mathrm{lin}{34.2}^{\circ }=$ eir e

$\frac{3}{2}\times \left(0.281\right)=\text{line}$

$e\leftarrow {57}^{\circ }={60}^{\circ }$

$\text{hence option A is congect}$