A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of $60 °$ (see figure). If the refractive index of the material of the prism is $\sqrt{3}$ , which of the following is (are) correct [2010]

Question

Smart Achievers · Accepted Answer

(1, 2, 3)

(1) Applying Snell's law at P,

$n_{1} \sin i = n_{2} \sin r$

$\Rightarrow n_{1} \sin 60 ° = n_{2} \sin θ$

$\Rightarrow \sin 60 ° = \sqrt{3} \sin θ$

$\Rightarrow θ = 30 ° = r$

In quadrilateral BCQP,

$60 ° + (90 ° + 30 °) + 135 ° + ∠ P Q C = 360 °$

$\Rightarrow ∠ P Q C = 45 °$ $\Rightarrow i = 45 °$

The critical angle for prism - air pair of media,

$C = \sin^{- 1} (\frac{1}{\sqrt{3}})$ which is less than $45 °$ .

Therefore, total internal reflection takes place at face CD.

(2) In $∆ Q D M$ , $∠ Q M D = 180 ° - (45 ° + 75 °) = 60 °$

Therefore, the angle of incidence of ray QM on AD is $30 ° .$

This angle is less than the critical angle. Hence the ray emerges out of face AD.

(3) From the figure, the angle between the incident ray OP and the emergent ray MR is $90 ° .$

Solution

Q.
A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of $60 °$ (see figure). If the refractive index of the material of the prism is $\sqrt{3}$ , which of the following is (are) correct [2010]

1 The ray gets totally internally reflected at face CD

2 The ray comes out through face AD

3 The angle between the incident ray and the emergent ray is $90 °$

4 The angle between the incident ray and the emergent ray is $120 °$

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