For a prism of apex angle 4 5 ∘ , it is found that the angle of emergence is 4 5 ∘ for grazing incidence. Calculate the refractive index of the prism.

Grazing incidence: sin r 1 = μ 1 , r 2 = 4 5 ∘ − r 1 sin 4 5 ∘ = μ sin ( 4 5 ∘ − r 1 ) = 2 1 ( μ 2 − 1 − 1 ) μ 2 − 1 = 2 μ = 5

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Physics - Geometrical Optics Question with Solution | TestHub

PhysicsGeometrical OpticsTIR/Prism and DispersionMedium2 minQB

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For a prism of apex angle $4 5^{\circ}$ , it is found that the angle of emergence is $4 5^{\circ}$ for grazing incidence. Calculate the refractive index of the prism.

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Answer:

Solution:

Grazing incidence: $sin r_{1} = \frac{1}{μ}$ , $r_{2} = 4 5^{\circ} - r_{1}$

$sin 4 5^{\circ} = μ sin (4 5^{\circ} - r_{1}) = \frac{1}{2} (μ^{2} - 1 - 1)$

$μ^{2} - 1 = 2$

$μ = 5$

Stream:JEESubject:PhysicsTopic:Geometrical OpticsSubtopic:TIR/Prism and Dispersion

⏱ 2mℹ️ Source: QB

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