Question

P1. Two layers of glass are placed on top of each other. The light is travelling
from n = 1.45 to n = 1.40. Find the range of angles , for which total internal reflection takes place.​

Answer 1

Critical angle is given by:

θ  

c

​  

=sin  

−1

(1/μ)

For ray 1,

i=45  

o

=sin  

−1

(  

1.414

1

​  

)

θ  

c1

​  

=sin  

−1

(  

1.35

1

​  

)>sin  

−1

(  

1.414

1

​  

)

Hence, θ  

c1

​  

>i

Ray will not undergo total internal reflection.

Applying snell's law,

1.35sin(45)=1sin(θ  

r

​  

)

sin(θ  

r

​  

)=0.9545

θ  

r

​  

≈72  

o

 

For ray 2,  

i=45  

o

=sin  

−1

(  

1.414

1

​  

)

θ  

c2

​  

=sin  

−1

(  

1.45

1

​  

)

θ  

c2

​  

=sin  

−1

(  

1.45

1

​  

)<sin  

−1

(  

1.414

1

​  

)

Hence, θ  

c1

​  

<i

Ray will undergo total internal reflection.