A luminous object O is located at the bottom of a big pool of liquid of refractive index `mu` and depth h. The object O emits rays upwards in all directions, so that a circle of light is formed at the surface of the liquid by the rays which are refracted into the air. what happens to the rays beyond the circle ? Determine the radius and the area of the circle .

Explanation

`musinC=1xxsin90^@`
`sinC=1//mu`
When `iltC`, rays are refracted into air
When `i=C`, `r=90^@`
`igtC`, T.I.R. takes place
`DeltaOAB`,

`sinC=(R)/(sqrt(h^2+R^2))`
`(1)/(mu)=(R)/(sqrt(h^2+R^2))`
`(1)/(mu^2)=(R^2)/(h^2+R^2)impliesh^2+R^2=mu^2R`
`(mu^2-1)R^2=h^2`
`R=(h)/(sqrt(mu^2-1))`