The refractive index of a material `M_1` changes by `0.014` and that of another material `M_2` changes by `0.024` as the colour of the light is changed from red to violet. Two thin prisms one made of `M_1 (A = 5.3^@)` and other made of `M_2(A = 3.7^@)` are combined with their refracting angles oppositely directed.
(a) Find the angular dispesion produced by the combination.
(b) the prisms are now combined with their refracting angles similarly directed. Find the angular dispersion produced by the combination.

Answer

`0.0146^(@), 0.163^(@)`

Explanation

`mu_(v) - mu_( r) = 0.014`,
`mu_(v)' - mu_( r)' = 0.024`
`A = 5.3^(@), A' = 3.7^(@)`
When refracting angles are oppositely directed .
net angular dispersion
`= (mu_(v) - mu_( r))A - (mu_(v)' - mu_(r )')A'`
`= 0.014 xx 5.3 - 0.024 xx 3.7`
`= 0.0742 - 0.0888 = - 0.0146^(@)`
When refracting angles are similarly directed,
angular dispersion `= (mu_(v) - mu_(r ))A + (mu_(v)' - mu_(r )')A'`
`= 0.0742 + 0.0888 = 0.163^(@)`