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Question
A thin prism of crown glass (μr = 1.515, μv = 1.525) and a thin prism of flint glass (μr = 1.612, μv = 1.632) are placed in contact with each other. Their refracting angles are 5.0° each and are similarly directed. Calculate the angular dispersion produced by the combination.
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Solution
For crown glass, we have:-
Refractive index for red colour, μcr = 1.515
Refractive index for violet colour, μcv = 1.525
For flint glass, we have:-
Refractive index for red colour, μfr = 1.612
Refractive index for violet colour,μfv = 1.632
Refracting angle, A = 5°
Let:-
δc = Angle of deviation for crown glass
δf = Angle of deviation for flint glass
As prisms are similarly directed and placed in contact with each other, the total deviation produced (δ) is given by
δ = δc + δf
= (μc - 1)A + (μf – 1)A
= (μc + μf – 2)A
For violet light, δv = (μcv + μfv – 2)A
For red light, δr = (μcr + μfr – 2)A
Now, we have:-
Angular dispersion of the combination:-
δv – δr = (μcv + μfv – 2)A – (μcr + μfr – 2)A
= (μcv + μfv – μcr – μfr) A
= (1.525 + 1.632 – 1.515 – 1.612)5
= 0.15°
So, the angular dispersion produced by the combination is 0.15°.
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