Sol. First we consider a ray incident at A. From Snell's law,

Fig.

1 × sin 45º = sin θ 2

sin θ 2 =

θ 2 = 30º

Let the angle φ = ∠ AOC denote the position of the point C on the curved surface.

∠ CAO = 60º

The critical angle for glass to air interface can be determined from Snell's law.

n sin C = 1 × sin 90º

sin C = =

C = 45º

Fig. Fig.

If total internal reflection has to place at the curved surface, angle θ 3 must be greater than the critical angle, C = 45º.

As θ 3 = 180º – φ – 60º, therefore, for no total internal reflection,

180º – φ – 60º < 45º

or φ > 75º

When the ray falls at O, the refracted ray will move radially out, without deviation. The normal rays do not suffer deviation.

Next we consider a ray to the right of O.

For no total internal reflection,

∠ A'CO < 45º

In Δ OA'C, ∠ OA'C + ∠ A'CO + ∠ COA' = 180º

120º + θ 4 + (180 – φ ) = 180º

θ 4 = φ – 120º

Thus, φ – 120º < 45º

φ < 165º

Hence for rays to transmit through curved surface,

75º < φ < 165º