Question

Answer this Question:- The refractive index of the glass prism shown in the figure (Attachment)is 2 for green light . A ray of cyan colour light incident at P on the face of BC of the prism. From which side would the light emerge? (Given critical angle for blue colour is greater than 15 degree.) Spam/Wrong answers will be deleted.

Answer 1

Given :

➳ Refractive index of glass prism for green light = 2

To Find :

➝ We have to find the side from which light would emerge$.$

Concept :

Critical angle and Total internal reflection (TIR) :

➠ Critical angle is the angle made in denser medium for which the angle of reflection in rarer medium is 90°.

➠ When angle in denser medium is more then critical angle the light ray reflects back in denser medium following the laws of reflection and the interface behaves like a perfectly reflecting mirror.

(Refer the first attachment for better understanding about TIR)

➠ Ray of cyan colour is the mixture of blue and green colour.

➠ Question is about ray of green light so, we won't consider ray of blue light. :D

Calculation :

ATQ, Refractive angle of prism for green light is 2.

We have to find critical angle for green light.

Let's calculate ☃

$\dashrightarrow\rm\:\sin\:C=\dfrac{1}{n}$

$\dashrightarrow\rm\:\sin\:C=\dfrac{1}{2}$

$\dashrightarrow\rm\:C=\sin^{-1}\dfrac{1}{2}$

$\dashrightarrow\underline{\boxed{\bf{\purple{C=30\degree}}}}$

፨ Now, Refer the second attachment. It shows ray path of green light.

So, Ray of green light will move in the direction of AB after TIR at surface AC.

Answer 2

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Given that: Refractive index for green $μ_g=2$

since, $\sin \theta _c=30°$

Thus, critical angle on $\theta _c=30°$

Incident angle on AC =45°

So blue will emerge out from AC and green will get internally reflected.

On face AB incident angle is 30° . So green will come out from AB.

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