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MCQMediumJEE 2026Prisms & Total Internal Reflection

JEE Physics 2026 Question with Solution

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface. If refractive index of the material of prism is 2\sqrt{2}, the angle θ\theta of prism is :

Prism diagram showing a horizontal incident ray entering the left face, internal refraction inside the prism, left base angle marked 45 degrees, and the right base angle marked theta.
  • A

    90∘90^\circ

  • B

    45∘45^\circ

  • C

    75∘75^\circ

  • D

    60∘60^\circ

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: The refractive index of the prism material is μ=2\mu = \sqrt{2}. The incident ray is parallel to the base of the prism, and the emergent ray grazes the second surface.

Find: The prism angle θ\theta.

When the emergent ray grazes the second surface, the internal angle of incidence at the second face is the critical angle.

sin⁡r2=1μ\sin r_2 = \frac{1}{\mu}

Substituting μ=2\mu = \sqrt{2},

sin⁡r2=12\sin r_2 = \frac{1}{\sqrt{2}}r2=45∘r_2 = 45^\circ

For a prism,

r1+r2=Ar_1 + r_2 = A

where A=θA = \theta.

From the given configuration used in the solution, the ray enters the first face normally, so

r1=0r_1 = 0

Therefore,

0+45∘=θ0 + 45^\circ = \thetaθ=45∘\theta = 45^\circ

Therefore, the angle of the prism is 45∘45^\circ, so the correct option is B.

Using the grazing condition

Given: The ray grazes the second face and μ=2\mu = \sqrt{2}.

Find: The prism angle θ\theta.

"Grazing along the second surface" means the refracted ray at the second face emerges along the surface itself. Hence the internal incidence there must equal the critical angle.

The critical-angle relation is

sin⁡θc=1μ\sin \theta_c = \frac{1}{\mu}

So,

sin⁡θc=12  ⟹  θc=45∘\sin \theta_c = \frac{1}{\sqrt{2}} \implies \theta_c = 45^\circ

Thus,

r2=45∘r_2 = 45^\circ

Now use the prism relation

r1+r2=θr_1 + r_2 = \theta

The provided solution takes the entry at the first face to be normal incidence, hence

r1=0r_1 = 0

Therefore,

θ=r1+r2=0+45∘=45∘\theta = r_1 + r_2 = 0 + 45^\circ = 45^\circ

Hence, the correct option is B.

Common mistakes

  • Taking the grazing condition at the second surface to mean the external angle is 45∘45^\circ is incorrect. Grazing means the internal angle of incidence equals the critical angle. First find the critical angle using sin⁡θc=1μ\sin \theta_c = \frac{1}{\mu}.

  • Using the prism relation incorrectly as r2−r1=Ar_2 - r_1 = A is wrong. For a prism, the correct relation is r1+r2=Ar_1 + r_2 = A. Add the two internal refraction angles to get the prism angle.

  • Confusing the prism angle θ\theta with an angle of incidence or emergence leads to the wrong option. The quantity asked is the geometric angle of the prism, not the angle the ray makes with a surface.

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