Question

White light enters horizontally into 60 degrees apex prism where n(red) = 1. and n(blue) = 1.3. what are the angles at which red and blue emerge from the prism with respect to the normal.

Answer 1

for red light e = -30 Degree

for Blue light e = 12.67 degree

Step-by-step explanation:

given data:

using prism formula for red light

`n =(sin90)/(sin r)`

`sin r = (1)/(n)`

`r =sin^(-1)* (1)/(n)`

`r =sin^(-1)* (1)/(1) = 90 Degree`

from figure

r+ r' = A

where A is 60 degree

r' = 60 - 90 = -30 degree

angle of emergence will be

`\mu = (sin e)/(sin r')`

`sin e =\mu * sin r'`

`e = sin^(-1) [-0.5* 1]`

e = -30 Degree

using prism formula for Blue light

`n =(sin90)/(sin r)`

`sin r = (1)/(n)`

`r =sin^(-1)* (1)/(n)`

`r =sin^(-1)* (1)/(1.3) = 50.28 Degree`

from figure

r+ r' = A

where A is 60 degree

r' = 60 - 50.28 = 9.72 degree

angle of emergence will be

`\mu = (sin e)/(sin r')`

`sin e =\mu * sin r'`

`e = sin^(-1) [sin(9.72)* 1.3]`

e = 12.67 Degree