A disc is placed on the surface of pond filled with liquid of refractive index `(5)/(3)`. A source of light is placed 4m below the surface of liquid. Calculate the minimum area of the disc so that light does not come out of liquid.

Explanation

`Sin C = (1)/(mu)`
or, `(r)/(sqrt(r^(2)+h^(2))) = (1)/(mu)`
or, `mu = (sqrt(r^(2)+h^(2)))/(r)`
or, `mu^(2) = (r^(2)+h^(2))/(r^(2)) = 1+(h^(2))/(r^(2))`
or, `(h^(2))/(r^(2)) = mu^(2) - 1`
or, `r = (h)/(sqrt(mu^(2)-1)) = (4)/(sqrt((25)/(9)-1)) = (4)/((4)/(3)) = 3m`
`:.` Required area of the disc `= pi r^(2) = 3.14 xx 9 m^(2) = 28.26 cm^(2)`