Consider the situation shown in the figure. Here θ is the maximum angle for which the light suffers total internal reflection at the vertical surface. Then sin θ will be:-

Step-by-step solution

The critical angle for this case is θ ″ = sin -1 1 1 . 2 5 = sin -1 4 5 or, sin θ ″ = 4 5 Since θ ″ = π 2 - θ ′ , we have sin θ ′ = cos θ ″ = 3 / 5 . From Snell's law, sin θ sin θ ′ = 1 . 2 5 or, sin θ = 1 . 2 5 × sin θ ′ = 1 . 2 5 × 3 5 = 3 4 or, θ = sin -1 3 4 . If θ ″ is greater than the critical angle, θ will be smaller than this value. Thus, the maximum value of θ , for which total reflection takes place at the vertical surface, is sin − 1 ( 3 / 4 ) .