Question: Q. 3. Three rays $(1,2,3)$ of different colours fall normally on one of the sides of an isosceles right angled prism as shown. The refractive index of prism for these rays is $1.39,1.47$ and 1.52 respectively. Find which of these rays get internally reflected and which get only refracted from AC. Trace the paths of rays. Justify your answer with the help of necessary calculations
U] [OD 2017]
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Solution:
Ans. At plane $A C$, the incident angle for ray 1 , ray 2 and ray $3=45^{\circ}$
Let critical angle for total internal reflection for ray $1=C_{1}$
$$ \begin{aligned} & 1=C_{1} \ & \Rightarrow \quad \sin C_{1}=\frac{1}{1.39} \ &=0.719 \end{aligned} $$
Hence $\quad C_{1}>45^{\circ} \quad(\sin 45=0.707)^{1 / 2}$
Let critical angle for total internal reflection for ray $2=C_{2}$
$$ \begin{align*} 1.47 & =\frac{1}{\sin C_{2}} \ \Rightarrow \quad \sin C_{2} & =\frac{1}{1.47}=0.68 \end{align*} $$
Hence $\quad C_{2}<45^{\circ}$
Let critical angle for total internal reflection for ray $3=\mathrm{C}_{3}$
$$ \begin{aligned} 1.52 & =\frac{1}{\sin C_{3}} \ \Rightarrow \quad \sin C_{3} & =\frac{1}{1.52}=0.657 \end{aligned} $$
Hence
$$ C_{3}<45^{\circ} $$
As in case of ray 1 , incident angle is less than critical angle, it would emerge out from $A C$. In the figure path of the ray 1 is shown.
In case of ray 2 , ray 3 , incident angle is greater than critical angle, they would get total internal reflection at $A C$ and emerge from $B C$. In the figure path of the ray 2 and 3 are shown.
$1 / 2$
