Question
Question: In the figure given below, for an angle of incidence \(45^\circ \) at the top surface, what is the m...
In the figure given below, for an angle of incidence 45∘ at the top surface, what is the minimum refractive index needed to total internal reflection at the vertical face?
A. 22+1
B. 21
C. 23
D. 2+1
Solution
Snell's law can be used here for the calculation of minimum refractive index for this problem. According to Snell's law sinrsini=n1n2, where i is angle of incidence and r is refracted angle and n1is refractive index of medium 1 and n2 is refractive index of medium 2.
Complete step by step solution:
Step 1:
It is given in the problem that the angle of incidence is 45∘,
So, according to Snell's law,
\dfrac{{\sin i{'}}}{{\sin r{'}}} = \dfrac{1}{\mu } \\
\Rightarrow \dfrac{{\sin i{'}}}{{\sin 90^\circ }} = \dfrac{1}{\mu } \\
\Rightarrow \mu \cdot \sin i{'} = \sin 90^\circ \\
\Rightarrow \mu \cdot \sin i{'} = 1 \\
\Rightarrow \sin i{'} = \dfrac{1}{\mu } \\