A ray of light is incident from air on a glass plate having thickness 3 cm and refractive index 2 . The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is _ _ _ _ × 10 - 2 cm . (given sin 15 ° = 0 . 26 )

Step-by-step solution

Let C be the critical angle. Then, sinC = 1 μ , where, μ is the refractive index of glass. So, sinC = 1 2 ⇒ C = 45 ° As the angle of incidence is equal to the critical angle, so using Snell's law, sinC = μ sin θ ⇒ 1 2 = 2   sin θ ⇒ θ = 30 ° Now, lateral displacement of the ray is x = t   sin ( i - r )   sec   r ⇒ x = 3 sin   45 ° - 30 ° sec   30 ° ⇒ x = 3 ( 0 . 26 ) 2 3 ⇒ x = 0 . 52   cm