Question

the refracting angle of a glass prism of refractive index 1.45 is 60 degrees. At what angle should a light ray be incident at the first face of the at prism so that it emerges at the second face just parallel to the face??​

Answer 1

The angle at which light ray should be incident is sin`−1(0.4).

Refractive index = ng = 1.45 (Given)

Temperature = A= 60° (Given)

e = 90° (Given)

r2=C (Critical angle)

sin C= 1/ng = sin r2 = 1/1.45 --- eq 1

Also,

sini/sin r1 = ng = 1.45

Thus, sin i = 1.45 × sin r1

Now, r1+r2 = A = 60°

or r1 = 60° −r2

Thus, sin i = 1.45 × sin (60°−r2)

Expanding the equation in 1st, -

i = sin−1 [1.45 × sin60 √1− 1/1.45²−cos 60°

= sin`−1(0.4)

Thus, the angle at which light ray should be incident is sin`−1(0.4).

Answer 2

Explanation:

angle of emergence is given 90°