Question

A point source of monochromatic light 'S' is kept at the centre C of the bottom of a cylinder. Radius of the circular base of the cylinder is 15.0 cm. The cylinder contains water (refractive index 4/3) to a height of 7.0 cm (see adjoining figure.

Find the area of water surface through which light emerges in air.

\((Take \,\pi =\frac{22}{7})\)

Answer 1

Given,

\(_a\mu_w =\frac{4}{3}\)

h = 7 cm

Sin C = \(\frac{1}{n}\)

\(=\frac{1}{4/3}=\frac{3}{4}\)

\(\therefore\, C=sin^{-1}(\frac{3}{4})=48.6°\)

From △OAS,

\(tan\,C=\frac{r}{h}\)

∵ r = h tan C

 = 7 x 1.13 = 7.94 cm

A = πr²

= π(7.94)² = 198 cm²