A point source of monochromatic light 'S' is kept at the centre of the bottom of a cylinder of radius `15.0 cm`. The cylinder contains water (refractive index 4//3) to a height of `7.0 cm`. Draw the ray diagram and calculate the area of water surface through which the light emerges in air.

Explanation

The light rays emerge through a circle of radius r from figure,
`r=h tan i_(c )=h((sini_(c ))/(cosi_(c )))`
`=(h.(1)/(mu))/(sqrt(1-(1)/(mu^(2))))=(h)/(sqrt(mu^(2)-1))`
`"Area of patch, "A=pir^(2)=(pih^(2))/(mu^(2)-1)`
`"Given, "h=7cm`
`mu=4//3`
`therefore" "A=(3.14xx7^(2))/((4//3)^(2)-1)`
`=3.14xx7^(2)xx(9)/(7)`
`=197.82cm^(2)`