Question

A point source of monochromatic light S is kept at the centre C of the bottom of a cylinder. The 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, as shown in the figure. Find the area of the surface through which light emerges in air. `("Take", π = 22/7)`

Answer 1

Given, μ = `4/3`

h = 7 cm

sin C = `1/μ`

sin C = `1/(4/3)`

sin C = `3/4`

C = `sin^-1(3/4)`

 C = 48.6°

From △OAS,

tan C = `r/h`

r = h × tan (48.6°)

= 7 × 1.134

= 7.938 cm

A = πr²

= `22/7 xx (7.938)^2`

= `22/7 xx 63`

= 198 cm²