Sol. The figure is drawn so that the ratio of the wall thickness t to the inner radius r is as large as possible. In this case the light from point P appears to be coming from P' at the edge. For thicker walls light from point P would appear to be coming from inside the edge. For thinner walls, light from point P could not be seen from this direction, and light apparently coming from P' would be originating at another point in the juice.

At this point the ray is tangential and will refract at critical angle φ C , in the glass; similarly at P' once again critical angle φ C is formed.

Critical angle at juice-glass interface,

sin φ C = , φ C = 62.73º

Critical angle at glass-air interface,

sin φ ' C = , φ ' C = 41.81º

From Δ OPM, sin θ = … (1)

From Δ PMP', tan φ ' C = … (2)

Where S = r – (d + t) = r – (r cos θ + t)

Angle φ C is exterior angle of triangle OPP'.

Hence θ + φ ' C = φ C

θ = φ C – φ ' C = 20.91º

Dividing eqn. (1) by (2), we get

= = 1 – cos θ +

= + cos θ – 1

On substituting numerical values, we get

= 0.33

Actual volume = π r 2 l

Apparent volume = π (r + t) 2 l

Hence =

=

= 1.77