The refractive indices of the crown glass for violet and red lights are`1.51`and `1.49`respectively and those of the flint glass are`1.77`and`1.73`respectively A prism of angle `6^(@)`is made of crown glass .A beam of white light is incident at a small angle on this prism.The other thin flint glass prism is combined white the crown glass prism such that te net mean deviation is`1.5^(@)`anticlockwise.
(i)Determine the angle of the flint glass prism.

(ii)A screen is placed normal to the emerging beam at a distance of`2m`from the prism combination.find the distance between red and violet spot on the screen Which is the topmost colour on screen.

Answer

`(1)2^(@)`,`(ii)(4pi)/(9)mm`

Explanation

(i) `delta_(C)=(mu_(y)-1)A`
`=((1.51+1.49)/(2)-1)6^(@)`
`delta_(C)=3^(@)(ACW)`
`delta_(F)'=(mu_(y)-1)A'(CW)`
`=((1.77+1.73)/(2)-1)A'`
`=(1.75-1)A'`
`delta_(F)'=0.75A'(C.W) rArr delta_(n et)=delta_(C)-S_(F)'(ACW)`
`1.5=3-0.75A'rArr 0.75A'=1.5rArr A'=2^(@)`
(ii)`delta_(V)=(mu-1)A+(mu_(y)-1)A'rArr delta_(v)=(1.51-1)6^(@)ACW+(1.77-1)2CW`
`=(3.06-1.54)ACW rArr delta_(v)=1.52ACW`
`delta_(R) =(mu_(R)-1)ACW+(mu_(R)^(')-1)ACW`
`=[(1.49-1)6^(@)-(1.73-1)2^(@)]`
`=1.48 ACW`
`(d_(2))/(D)=tandelta_(V)`
`(d_(1))/(D)=tandelta_(R) rArr d_(2)-d_(1)=D(delta_(V)-delta_(R))`
`d_(2)-d_(1)=2(1.52-1.48)m rArr d_(2)-d_(1)=2xx0.04xx(pi)/(180)m`
`(4pi)/(9)`