A combination of two prisms, one of flint and other of crown glass produces dispersion without deviation. The angle of flint glass prism is `15^@`. Calculate the angle of crown glass prism and angular separation of red and violet rays on emergence from the spectroscope. (`mu` for crown glass `= 1.52, mu` for flint glass `= 1.65, omega` for crown glass `= 0.02, omega` for flint glass `= 0.03`).

Explanation

Here, `A = 15^@, A' = ?, omega = 0.03`
`omega' = 0.02, mu = 1.65, mu' = 1.52`
For no deviation, `delta + delta' = 0`
`(mu - 1) A + (mu' - 1)A' = 0`
`(1.65 - 1) 15^@ + (1.52 - 1) A' = 0`
`A' = (-0.65 xx 15)/(0.52) = -18.75^@`
Negative sign indicates that two prisms must be joined in opposition.
Net angular separation
=`(mu_v - mu_r)A +(mu'_v - mu'_r)A'`
=`omega(mu - 1) A + omega' (mu' - 1)A'`
=`0.03(1.65 - 1)15^@ + 0.02(1.52 - 1)(-18.75^@)`
=`0.2925 - 0.195`
=`0.0975^@`.