Qstnid -Iv-9-a Thin Prism Of Crown Glass (Μ<sub>r</sub> = 1.515, Μ<sub>v</sub> = 1.525) And A Thin Prism Of Flint Glass (Μ<sub>r</sub> = 1.612, Μ<sub>v</sub> = 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. - 20: Dispersion And Spectra - Neet-xii-physics

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NEET-XII-Physics

20: dispersion and Spectra

with Solutions - page 4

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#9
A thin prism of crown glass (μ_r = 1.515, μ_v = 1.525) and a thin prism of flint glass (μ_r = 1.612, μ_v = 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.
Ans :
For crown glass, we have:
Refractive index for red colour, μ_cr = 1.515
Refractive index for violet colour, μ_cv = 1.525
For flint glass, we have:
Refractive index for red colour, μ_fr = 1.612
Refractive index for violet colour,μ_fv = 1.632
Refracting angle, A = 5°
Let:
δ_c = Angle of deviation for crown glass
δ_f= Angle of deviation for flint glass
As prisms are similarly directed and placed in contact with each other, the total deviation produced `` \left(\delta \right)`` is given by
δ = δ_c + δ_f
= (`` {\mu }_{c}`` - 1)A + (`` {\mu }_{f}`` - 1)A
= (`` {\mu }_{c}`` + `` {\mu }_{f}``- 2)A
For violet light, δ_v = (μ_cv + μ_fv - 2)A
For red light, δ_r= (μ_cr + μ_fr - 2)A
Now, we have:
Angular dispersion of the combination:
δ_v - δ_r= (μ_cv + μ_fv - 2)A - (μ_cr + μ_fr - 2)A
= (μ_cv + μ_fv - μ_cr - μ_fr) 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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