Question

the base angles of a triangular glass prism are alpha=30 degrees and its refractive index n=root 2 parallel rays are as shown in figure are normally incident on its base what is the angle between two emergent rays?
​

Answer 1

30  

∘

 

from Snell's Law,  

sin r  

1

​  

 

sin i

​  

=  

3

2

​  

 

​  

 

i=45  

∘

(by geometry)

sin r  

1

​  

 

sin 45  

∘

 

​  

=  

3

2

​  

 

​  

 

sinr  

1

​  

=  

2

3

​  

 

​  

 

r  

1

​  

=60  

∘

 

Let deviation for first ray be L  

1

​  

 and deviation for second ray be L  

2

​  

 

L  

1

​  

=60−45  

∘

 =15  

∘

 

Similarly, L  

2

​  

=15  

∘

 

∴ Angle between emergent rays =15+15 =30  

∘

 

​

Answer 2

The angle between two emergent rays is 30°.

Given:-

The base angles of the triangle = 30°

Refractive Index = √2

To Find:-

The angle between two emergent rays.

Solution:-

We can easily find out the angle between two emergent rays by using these simple steps.

As

The base angles of the triangle (a) = 30°

Refractive Index (n) = √2

Let the incidence angle be i, refractive index be r1 and r2.

incidence angle (i) = 90-30 = 60°

Here, according to the formula of Snell's law of refraction,

$\frac{ \sin(i) }{ \sin(r1) } = \sqrt{2}$

$\frac{ \sin(60) }{ \sin(r1) } = \sqrt{2}$

on solving we get, r1 = 15°

So, the deviation caused by one single ray = 30-15 = 15°

and

the deviation caused by two rays = 2×15 = 30°

Hence, The angle between two emergent rays is 30°.

#SPJ5