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# 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)NA of S1 immersed in water is the same as that of S2 immersed in a liquid of refractive index 163√15NA of S1 immersed in liquid of refractive index 6√15 is the same as that of S2 immersed in waterNA of S1 placed in air is the same as that of S2 immersed in liquid of refractive index 4√15NA of S1 placed in air is the same as that of S2 laced in water

A
NA of S1 placed in air is the same as that of S2 immersed in liquid of refractive index 415
B
NA of S1 immersed in water is the same as that of S2 immersed in a liquid of refractive index 16315
C
NA of S1 placed in air is the same as that of S2 laced in water
D
NA of S1 immersed in liquid of refractive index 615 is the same as that of S2 immersed in water
Solution
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#### Case−1 S1 immersed in air n1=√454n2=75 (1) sin1=√454sinγ→sin2i=(454)2(1−cos2γ) (√454)cosγ⩾(75)1−1645sin2i=cos2x−(1) Squaring 451412cos2γ⩾492545(4)2(1−1645sin2i)⩾492545(4)2−4sin2i4⩾49254516−4925⩾sin2i Case − (2) S 2 immersed in water. 43sini=√454sinγ169sin2i=4516sin2γ⇒1−(16)29(45)sin21=cos2γ4516cos2γ⩾49254516[1−(16)29(45)sin21]⩾,4925⇒4516−4925⩾sin2i So option c is correct

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