A container contains water up to a height of 20 cm and there is a point source at the centre of the bottom of the container. A rubber ring of radius r floats centrally on the water. The ceiling of the room is 2.0 m above the water surface. (a) Find the radius of the shadow of the ring formed on the ceiling if r = 15 cm. (b) Find the maximum value of r for which the shadow of the ring is formed on the ceiling. Refractive index of water =4/3.

Answer

A, B, C

Explanation

a. Using Snell's Law,
`mu_1sintheta_1=mu_2sintheta_2`
`rarr 4/3.15/(sqrt(400+25)=1. x/(sqrtx^2+(200)^2)`
`rarr 16.[x^2+(200)^2]=25x^2` ltBrgt `rarr 9x^215xx(200)^2`
`-x^2=15/9xx(200)^2`
`- x=4/3xx200cm

`:. Radius of the shadow
`=(800/3+15)`cm
`=845/3cm`
`=281.66cm`
`=2.8m`
`b. Using shells law
`mu_1sintheta_1=mu_2sintheta_2`
`rarr 4/3.r_m(sqrt(r_m^2+(20)^2)=1.sin90^@`
`rarr 4/3r_m=9[r_m^2=(20)^2]`
`rarr 7r_m^2=9xx(20)^2`
`- r_m=sqrt(9/7x(20)^2)`
`=(3xx20)/2.64=22.7cm`