Question

The dispersive powers of flint glass and crown glass are 0.053 and 0.034, respectively and their mean refractive indices are 1.68 and 1.53 for white light. Calculate the angle of the flint glass prism required to form an achromatic combination with a crown glass prism of refracting angle 4°:

Options

• 2°

• 4°

• 5°

• 6°

Answer 1

2°

Explanation:

Given

Flint glass	Crown glass
ωf = 0.053	ωc = 0.034
μf = 1.68	μc = 1.53
Af = ?	Ac = 4°

For no dispersion

ω_f d_f - ω_c d_c = 0

or ω_f A_f (μ_f - 1) = ω_cA_c(μ_c - 1) = 0

A_f = `(omega_"c""A"_"c"(mu_c-1))/(omega_"f"(mu_"f" -1))`

= `(0.034xx4°(1.53-1))/(0.053xx(1.68-1))`

= `(0.034xx4xx0.53)/(0.053xx0.68)`

⇒ A_f = 2°