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Figures 9.34(a) and (b) show refraction of a ray in air incident at 60° with the normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in glass when the angle of incidence in water is 45s with the normal to a water- glass interface [Fig. 9.34(c)].

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Class 12 Physics
CBSE and UP Board
Ray Optics and Optical Instruments
Chapter-9 Exercise 9.4
NCERT Solutions for Class 12 Physics Chapter 9 Question-4

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1 Answer

  1. As per the given figure, for the glass – air interface:

    Angle of incidence, i = 60°

    Angle of refraction, r = 35°

    The relative refractive index of glass with respect to air is given by Snell’s law as:

    μga= sin i/sin r

    = sin 60°/sin 35°= 0.8660/0.5736 = 1.51 ————–Eq-1

    As per the given figure, for the air-water interface:

    Angle of incidence, i = 60°

    Angle of refraction  r= 47°

    The relative refractive index of water with respect to air is given by Snell’s law as :

    μwa= sin i/sin r

    = sin 60°/sin 47°= 0.8660/0.7314 = 1.184————–Eq-2

    Using (1) and (2), the relative refractive index of glass with respect to water can be obtained as:

    μgw = μga/μwa

    =1.51/1.184= 1.275

    The following figure shows the situation involving the glass – water interface.

    Angle of incidence, i = 45°

    Angle of refraction = r

    From Snell’s law, r can be calculated as:

    sin i/sin r= μgw

    =>sin 45°/sin r = 1.275

    sin r = (1/√2)/1.275 = 0.5546

    Therefore ,r = sin⁻¹ (0.5546)

    = 38.68°

    Hence, the angle of refraction at the water – glass interface is 38.68°.

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