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PhysicsMultiple correct+3Question 68 of 84

IIT-JEE 2010 · Paper 1, Physics question 68

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 3\sqrt3, which of the following is (are) correct?

A four-sided prism ABCD: AB vertical on the left, AD the base; angles B = 60°, C = 135°, A = 90°, D = 75°. A ray from O strikes face AB at P near B.
Choose one or more options
Answer and worked solution

Official answer: A, B, C

Entry at AB. sin⁡60°=3sin⁡r\sin60°=\sqrt3\sin r gives r=30°r=30°. The critical angle is sin⁡−113≈35.3°\sin^{-1}\frac1{\sqrt3}\approx35.3°.

Geometry. Going round A → B → C → D with interior angles 90°, 60°, 135°, 75°: with AD horizontal and AB vertical, side BC slopes down at 30° below the horizontal and CD at 75° below it. The refracted ray (30° below the normal of AB, i.e. 30° below the horizontal) runs parallel to BC.

At CD. The normal to CD is at 15° above the horizontal, so the angle of incidence is 15°+30°=45°>35.3°15°+30°=45°>35.3°: total internal reflection. (A) true.

After reflection the ray travels at 120° below the horizontal (down and to the left) and meets the base AD at 30°30° to its normal, less than the critical angle: it emerges through AD, refracted to sin⁡−1(3sin⁡30°)=60°\sin^{-1}(\sqrt3\sin30°)=60° from the normal. (B) true.

Deviation. The incident ray travels at 60° below the horizontal (heading right); the emergent ray at 150° below it (heading left and down). The angle between them is 90°. (C) true, (D) false.

(A), (B), (C)

Topics:Total internal reflectionPrism and dispersionRefraction at plane surfaces
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