Physics - Geometrical Optics Question with Solution | TestHub

PhysicsGeometrical OpticsTIR/Prism and DispersionEasy2 minPYQ_2020

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A ray of light passing through a prism of refractive index $\sqrt{2}$ undergoes minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. The angle of the prism is

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Answer:

Solution:

According to given problem, $i = 2 r = A$

$(∵ a n g l e o f p r i s m, A = 2 r)$

Since, $δ_{m} = 2 i - A$

$\Rightarrow δ_{m} = 2 A - A = A$

We have, $n = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})} \Rightarrow \sqrt{2} = \frac{\sin A}{\sin (\frac{A}{2})}$

$\Rightarrow \sqrt{2} = \frac{2 \sin (\frac{A}{2}) \cos (\frac{A}{2})}{\sin (\frac{A}{2})}$

$\Rightarrow \cos (\frac{A}{2}) = \frac{\sqrt{2}}{2} \Rightarrow \frac{A}{2} = \cos^{- 1} (\frac{1}{\sqrt{2}})$

$\Rightarrow \frac{A}{2} = 45 ° \Rightarrow A = 90 °$

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

⏱ 2mℹ️ Source: PYQ_2020

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