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.

Answer

`198.0 cm^(2)`

Explanation

Here, `R = 15.0 cm, mu = 4//3, h = 7.0 cm`.

As is clear from Fig. light rays emerge through a circle of radius `r`.
`r = h tan C` …(i)
where `sin C = (1)/(mu) = (1)/(4//3) = (3)/(4)` ,
`cos C = sqrt(1 - (3//4)^(2)) = (sqrt(7))/(4)`
`tanC = (3)/(4) xx (4)/(sqrt(7)) = (3)/(sqrt(7))`
Area of path through which light emerges
`= pir^(2) = pi (h tan C)^(2) pi h^(2) tan^(2)C`
`= (22)/(7) xx 7 xx((3)/(sqrt(7)))^(2) = 198.0 cm^(2)`