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Question

# A right angled prism of refractive index μ1 is placed in a rectangular block of refractive index μ2, which is surrounded by a medium of refractive index μ3, as shown in the figure. A ray of light ′e′ enters the rectangular block at normal incidence. Depending upon the relationship between μ1,μ2 and μ3, it takes one of the four possible paths ′ef′,′eg′,′eh′ or ′ei′. Match the paths in List -I with conditions of refractive indices in List -II and choose the correct answer. List - I List - II (P) e→f (1) μ1>√2μ2 (Q) e→g (2) μ2>μ1 & μ2>μ3 (R) e→h (3) μ1=μ2=μ3 (S) e→i (4) μ2<μ1<√2μ2 & μ2>μ1

A
P-2 , Q-3 , R-1 , S-4
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B
P-1 , Q-2 , R-4 , S-3
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C
P-4 , Q-1 , R-2 , S-3
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D
P-2 , Q-3 , R-4 , S-1
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Solution

## The correct option is D P-2 , Q-3 , R-4 , S-1 The given figure, Case (P): When ray travelling along the path ′ef ′ : At the surface of prism, ray is moving towards normal MN so, we can conclude that , μ2>μ1. At the surface of block, ray moving away from normal PQ so, μ3<μ2. Hence, P matches with (2). Case (Q): When ray travelling along the path ′eg ′ There is no deviation of rays on both surfaces, so it is clearly evident from ray diagram that , μ1=μ2=μ3 Hence, Q matches with (3) Case (R): When ray is travelling along the path ′eh ′ At the prism surface ray moving away from normal MN. so, we can conclude that , μ2<μ1. At block surface , ray is moving away from normal PQ. so , we can conclude that , μ3<μ2 but total internal reflection does not take place on prism surface. So , μ1sin45∘>μ2sin90∘ ∴μ1>√2μ2 Hence, R matches with (4). Case (S):When ray is travelling along the path 'ei' Total internal reflection takes place at the surface of prism . so, μ1sin45∘<μ2sin90∘ ∴μ1>√2μ2. Hence, S matches with (1) Thus, option (d) is the correct answer.

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