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

C, D

Explanation

For no deviation condition
`A^`=[(mu-1]/mu^`]A`
`impliesA^`=(1.5-1)/(1.75-1)xx6^circ=4^circ`
Now the angular dispersion produced by crown glass prism
`delta_b-delta_r=A(mu_b-mu_r)`
Also the angular dispersion produced by flint glass prism
`delta_b^`-delta_r^`=A^`(mu_b^`-mu_r^`)`
`:'``Net deviation in blue light
`delta_b=(mu_(b1-1))A_1-(mu_(b2)-1)A_2` `=(1.51-1)6^circ-(1.77-1)4^circ=-0.02^circ`
Similarly Net deviation of red light
`delta_r=(mu_n-1)A_1-(mu_(r2)-1)A_2`
`=(1.49-1)6^circ-(1.73-1)4^circ=-0.04^circ`
`:'` The magnitude of the net angular dispersion`=0.04`
`:'` The magnitude of the net angular dispersion`=0.04`