A small bulb (assumed to be a point source) is placed at the bottom of a tank containing water to a depth of `80 cm`. Find out the area of the surface of water through which light from thr bulb can emerge. Take the value of refractive index of water to be `4//3`.

Explanation

`h=80cm=0.8m`
`i_(c )` is critical angle.
The rays of light from small bulb S will emerge along the surface if they are incident at critical angle.
`tani_(c )=(r )/(h)rArr =h tan i_(c )`
`sin i_(c )=(1)/(mu)=(1)/(1.33)=(3)/(4)`
`cosi_(c )=sqrt(1-(sini_(c))^(2))`
`=sqrt(1-((3)/(4))^(2))=sqrt((7)/(16))`
`tani_(c )=(sini_(c ))/(cosi_(c ))=(3)/(4)xx(4)/(sqrt7)=(3)/(sqrt7)`
`"As area "=pir^(2)=pi(h tan i_(c))^(2)`
`=3.14xx(0.80)^(2)xx((3)/(sqrt7))^(2)`
`=(18)/(7)=2.58m^(2).`