A glass plate having parallel faces and a refractive index o

A glass plate having parallel faces and a refractive index of 1.57 lies at the bottom of a liquid of refractive index 1.66. A ray of light in the liquid strikes the top of the glass at an angle of incidence of 60.0 degree. Compute the angle of refraction of this light in the glass.

Solution

Index of refraction of liquid n = 1.57

Index of refraction of glass n \' = 1.66

Angle of incidenceon the top of the glass i = 60 ^o

Angle of refraction of light in the glass r = ?

From Snell\'s law sin i / sin r = n \' / n

                      sin 60 / sin r = 1.66 / 1.57

                                         = 1.0573

                                 sin r = sin 60 / 1.0573

                                        = 0.866 / 1.0573

                                       = 0.819

                                   r = sin ^-1 (0.819)

                                      = 55 ^o