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 light is incident on one face at an angle of incident, which gives minimum deviation for red light. Find :
(a) the angle of incidence
(b) angular width of the spectrum
(c) the length of the spectrum if it is focussed on a screen by lens focal length `100 cm`.
[Use: `sin (49.7^(@)) =0.760, sin (31.6^(@))=0.520 , sin (28.4^(@))=0.475, sin (56^(@))=0.882 , pi =22//7`]

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`