Question

Suppose a red laser beam (n = 1.49) were incident on an equilateral prism at an angle of 50.0

Answer 1

all following the formula , Nmedium1 * sin i = Nmedium2 * sin r

for red n = 1.49
nair sin 50 = nglass sin r
sinr = 0.514
r = 30.93

on the far end of glass angle of incidence = 60 - 30.93 = 29.07 (this is because if you take the diagram of the prism, then you will find the angle of incidence on the far side of the glass that is inside the glass to be 60 degree - r )
so 1.49 sin 29.07 = 1 sin e
=> sin e = 0.724
e = 46.38 degree

for the blue light
nair sin 50 = nglass sin r
=> sin r = sin 50 / 1.53 = 0.5
=> r = 30 degree

now for the farther side

angle of incidence = 60-30 = 30

1.53 sin 30 = 1 sin e

sin e = 0.765
e = 49.9 degree

difference in the angle of emergrence = 49.9 - 46.38 = 3.52 degree