Ray Optics and Optical Instruments Part 1

Given
Dispersive power of crown glass, ω1=0.02
Dispersive power of flint glass, ω2=0.03
Refractive index of yellow light,
for crown glass, µ1=1.5 and
for flint glass, µ2=1.6
This is a case of achromatic combination.
∴‌‌θ‌net ‌=0
⇒‌‌θ1−θ2=0⇒θ1=θ2
⇒‌‌ω1δ1=ω2δ2‌‌[∵θ=ωδ]... (i)
and δ‌net ‌=δ1−δ2=2∘......(ii)
From Eqs. (i) and (ii), we get
δ1−‌

ω1δ1

ω2

=2∘
⇒‌‌δ1(1−‌

ω1

ω2

)=2∘⇒δ1(1−‌

2

3

)=2∘
⇒‌‌δ1=6∘
Also, δ1=(µ1−1)A1
⇒‌‌6∘=(1.5−1)A1⇒A1=12∘
∴ The refracting angle for crown glass prism will be 12∘.