Question

A flint glass prism and a crown glass prism are to be combined in such a way that the deviation of the mean ray is zero. The refractive index of flint and crown glasses for the mean ray are 1.620 and 1.518 respectively. If the refracting angle of the flint prism is 6.0°, what would be the refracting angle of the crown prism?

Answer 1

Given:
Refractive index of the flint glass, μ_f = 1.620
Refractive index of the crown glass, μ_c = 1.518
Refractive angle of the flint prism, A_f = 6°
Now,
Let the refractive angle of the crown prism be A_c.
For the net deviation of the mean ray to be zero,
Deviation by the flint prism = Deviation by the crown prism
i.e., (μ_f − 1)A_f = (μ_c − 1)A_e
$\Rightarrow A_c=\left(\frac{{\mu }_{\mathrm{f}}-1}{{\mu }_{\mathrm{e}}-1}\right)A_{\mathrm{f}}$
$\Rightarrow A_{\mathrm{c}}=\left(\frac{1.620-1}{1.518-1}\right)\times 6.0°=7.2°$

Thus, the refracting angle of the crown prism is 7.2$°$.