A glass prism with a refracting angle of `60^(@)` has a refractive index 1.52 for red and 1.6 for violet light. A parallel beam of white is incident on one face at an angle of incident which gives minimum deviation for red light. Find :
[Use : `sin(50^(@))=0.760 , sin(31.6^(@))=0.520 , sin (28.4^(@))=0.475 , sin (56^(@))= 0.832 , = 22//7`]
The angle of incidence at the prism is :

Answer

(a) `49.7^(@)`,(b) `56^(@)-49.7^(@)=6.3^(@)` (c) `ftheta=11c m`

Explanation

(a) `mu_(R)=1.52`
`mu_(v)=1.6`
Minimum deviation condition for red is `r=30^(@)`
`rArr (1)sini=(1.52) sin30^(@)`
`i=49.7^(@), delta_(R)=(49.7)2-60^(@)`
`=39.4^(@)`
(b) For violet light `(1) sin 49.7^(@)=(1.6)sin r`
`therefore r=28.4^(@)`
`r=31.6^(@) (because r+r'=A)`
`(1) sin e =(1.6) sin 31.6^(@)`
`therefore e=56^(@)`
`rArr delta_(v)=i+e-A=49.7^(@)+56^(@)-60^(@)`
`45.7^(@)`
`therefore` angular width `=delta_(v)-delta_(R)`
`=6.3^(@)`
(c) `f theta=100xx6.3^(@)xx(pi)/(180^(@)) cm=11 cm`