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Question

For two structure namely S1 with n1=45/4 and S2 with n1=8/5 and n2=7/5 and taking the refractive index of water to be 4/3 and that of air to be 1, the correct option(s) is (are)
1011288_39ed3bb2a6484e18a5e131eda04fcb67.png
  1. NA of S1 immersed in water is the same as that of S2 immersed in a liquid of refractive index 16315
  2. NA of S1 immersed in liquid of refractive index 615 is the same as that of S2 immersed in water
  3. NA of S1 placed in air is the same as that of S2 immersed in liquid of refractive index 415
  4. NA of S1 placed in air is the same as that of S2 laced in water

A
NA of S1 immersed in liquid of refractive index 615 is the same as that of S2 immersed in water
B
NA of S1 placed in air is the same as that of S2 immersed in liquid of refractive index 415
C
NA of S1 immersed in water is the same as that of S2 immersed in a liquid of refractive index 16315
D
NA of S1 placed in air is the same as that of S2 laced in water
Solution
Verified by Toppr

Case1
S1 immersed in air

n1=454n2=75

(1) sin1=454sinγsin2i=(454)2(1cos2γ)

(454)cosγ(75)11645sin2i=cos2x(1) Squaring
451412cos2γ492545(4)2(11645sin2i)492545(4)24sin2i4492545164925sin2i



Case (2) S 2 immersed in water.

43sini=454sinγ169sin2i=4516sin2γ1(16)29(45)sin21=cos2γ4516cos2γ49254516[1(16)29(45)sin21],492545164925sin2i So option c is correct

2005776_1011288_ans_6d0845441eb44987a55e19d0de5c24e3.PNG

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