A ray in glass is incident onto a waterglass interface at an

A ray in glass is incident onto a water-glass interface, at an angle of incidence equal to half the critical angle for that interface. The indices of refraction for water and the giass are 1.33 and 1.80, respectively. The angle that the refracted ray in the water makes with the normal is closest to: C) 38 A) 430 B) 23 D) 330 E) 28

Solution

Snell\'s law

n1*sin A1 = n2*sin A2

1.80*sin A1 = 1.33*sin 90

A1 = arcsin(1.33/1.80) = 47.63 deg

by given condition

n1*sin (A1/2) = n3*sin A3

A3 = arcsin(1.80*sin (23.815 deg)/1.33) = 33.12 deg

Ans is option D 33 deg

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