Ray Optics

JEE Main level, single correct, medium

240 of 295

Question 240 of 295

Consider an equilateral prism (refractive index 2\sqrt{2}). A ray of light is incident on its one surface at a certain angle ii. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ____\_\_\_\_.

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Answer: (B) 15∘15^{\circ}

Given an equilateral prism, the angle of the prism is A=60∘A = 60^{\circ}.
The refractive index of the prism is μ=2\mu = \sqrt{2}.
The emergent ray grazes the second surface, which means the angle of emergence is e=90∘e = 90^{\circ}.
Applying Snell's law at the second surface: μsin⁡(r2)=1⋅sin⁡(e)\mu \sin(r_2) = 1 \cdot \sin(e).
2sin⁡(r2)=sin⁡(90∘)=1\sqrt{2} \sin(r_2) = \sin(90^{\circ}) = 1.
sin⁡(r2)=12\sin(r_2) = \frac{1}{\sqrt{2}}, which gives r2=45∘r_2 = 45^{\circ}.
For a prism, we know the relation r1+r2=Ar_1 + r_2 = A.
Substituting the values: r1+45∘=60∘r_1 + 45^{\circ} = 60^{\circ}.
r1=60∘−45∘=15∘r_1 = 60^{\circ} - 45^{\circ} = 15^{\circ}.
The angle of refraction at the incident surface is r1=15∘r_1 = 15^{\circ}.

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