Answer to Question #103249 in Optics for saurabh pandey

Question

A ray EF of monochromatic light is incident on the refracting AB of a regular glass prism(refractive index=1.5)at an angle of incidence i=55°.if it emerges through the adjacent face AC..calculate angle of emergence

Answer 1

As per the question,

Refractive index of the prism $(\mu)=1.5$

Angle of incidence (i)$= 55^\circ$

As per the question, the prism is the regular glass prism, So the prism angle (A)=$60^\circ$

Let the angle of deviation of the light $\delta_{min},$ and angle of emergence = e

We know that

$\Rightarrow \dfrac{\sin{\dfrac{A+\delta}{2}}}{\sin{\dfrac{A}{2}}}=\mu$

$\Rightarrow \dfrac{\sin{\dfrac{60+\delta}{2}}}{\sin{\dfrac{60}{2}}}=1.5$

$\Rightarrow \dfrac{\sin{\dfrac{A+\delta}{2}}}{\sin{30}}=1.5$

$\Rightarrow 2\sin{\dfrac{A+\delta}{2}}=1.5$

$\Rightarrow \sin{(30+\delta/2)}=\dfrac{3}{4}$

$\Rightarrow 30+\delta/2=48.6^\circ$

$\Rightarrow \delta/2=48.6^\circ-30^\circ=18.6^\circ$

$\Rightarrow \delta=37.2^\circ$

We know that, for the prism,

$i+e=A+\delta$

$\Rightarrow e=A+\delta-i$

$\Rightarrow e=60+37.2-55=42.2^\circ$

Hence, the angle of emergent will be $42.2^\circ$