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Question
Solve Numerical example.
From the given data set, determine angular dispersion by the prism and dispersive power of its material for extreme colours. nR = 1.62 nV = 1.66, δR = 3.1°
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Solution
Given: nR = 1.62, nV = 1.66, δR = 3.1°
To find: i. Angular dispersion (δVR)
ii. Dispersive power (ωVR)
Formula: i. δ = A (n − 1)
ii. δVR = δV − δR
iii. ω = `(δ_"V"-δ_"R")/(((δ_"V"+δ_"R")/2))`
Calculation: From formula (i),
δR = A(nR − 1)
∴ A = `δ_"R"/(("n"_"R"-1))=3.1/((1.62-1))=3.1/0.62`
∴ δV = A(nV − 1) = 5 × (1.66 − 1) = 3.3°
From formula (ii),
δVR = 3.3 − 3.1 = 0.2°
From formula (iii),
ωVR = `(3.3-3.1)/(((3.3+3.1)/2))=0.2/6.4xx2=0.2/3.2=1/16`
= 0.0625
- Angular dispersion by prism is 0.2°
- Dispersive power of material of prism is 0.0625.
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