An achromatic combination of two prisms - one of quartz and other of flint glass is to be formed. If the refracting angle of the quartz prism is 4°, find the refracting angle of the flint glass prism. Also find the net mean deviation produced by the combination. Given that for the flint glass : $μ_v = 1.694, μ_r = 1.65$ and for the quartz glass : $μ_v = 1.557, μ_r = 1.542$.

–1.282

For an achromatic combination, net dispersion = 0

⇒ dispersion by one prism = dispersion by other prism.

$⇒(μ_{1v}-μ_{1r})A_1=(μ_{2v}-μ_{2r})A_2$

$⇒(1.694 − 1.65)A_1=(1.557 − 1.542) × 4$

$⇒A_1=1.364°$

$D_{m1}-D_{m2}=(μ_{1m}-1)A_1-(μ_{2m}-1)A_2$

$=(\frac{μ_{1v}+μ_{1r}}{2}-1)× 1.364 −(\frac{1.557 + 1.542}{2}-1)× 4$

$= - 1.641° × 2 = - 1.282$

Net mean deviation = $|D_{m1}-D_{m2}|=−1.282$