air refactive index n a = 1.00029
water refractive index n w = 1.33
refractive index of a glass prism n =1.52
incident angle on AC surface i = 90 - α
for without any light refracted out of the prism at face AC
,refracted angle r = 90
o
from snell's law ( sin i / sin r ) = ( n 2 / n 1 )
here i = 90 - α
r = 90
n 2 = n a = 1.00029
n 1 = n = 1.52
substitute these values in above, we get
( sin ( 90 - α ) / sin 90 ) = (1.00029 / 1.52 )
=
0.658
sin ( 90 - α ) = 0.658
90
- α = sin -1 ( 0.658 )
=
41.15
α
= 90 - 41.15
=
48.85 o
( b ) . when prism immerssed in water
from snell's law ( sin i / sin r ) = ( n 2 / n 1 )
here i = 90 - α
r = 90
n 2 = n w = 1.33
n 1 = n = 1.52
substitute these values in above, we get
( sin ( 90 - α ) / sin 90 ) = (1.33 / 1.52 )
=
0.875
sin ( 90 - α ) = 0.875
90
- α = sin -1 ( 0.875 )
=
61
α
= 90 - 61
=
29 o