Answer:
for red light e = -30 Degree
for Blue light e = 12.67 degree
Explanation:
given data:
using prism formula for red light
[tex]n =\frac{sin90}{sin r}[/tex]
[tex]sin r = \frac{1}{n}[/tex]
[tex]r =sin^{-1}\times \frac{1}{n}[/tex]
[tex]r =sin^{-1}\times \frac{1}{1} = 90 Degree[/tex]
from figure
r+ r' = A
where A is 60 degree
r' = 60 - 90 = -30 degree
angle of emergence will be
[tex]\mu = \frac{sin e}{sin r'}[/tex]
[tex]sin e =\mu \times sin r'[/tex]
[tex]e = sin^{-1} [-0.5\times 1][/tex]
e = -30 Degree
using prism formula for Blue light
[tex]n =\frac{sin90}{sin r}[/tex]
[tex]sin r = \frac{1}{n}[/tex]
[tex]r =sin^{-1}\times \frac{1}{n}[/tex]
[tex]r =sin^{-1}\times \frac{1}{1.3} = 50.28 Degree[/tex]
from figure
r+ r' = A
where A is 60 degree
r' = 60 - 50.28 = 9.72 degree
angle of emergence will be
[tex]\mu = \frac{sin e}{sin r'}[/tex]
[tex]sin e =\mu \times sin r'[/tex]
[tex]e = sin^{-1} [sin(9.72)\times 1.3][/tex]
e = 12.67 Degree
