A horizontal cylinderical tank `(6)/(pi)m` in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved bottom of the water and aims a light beam towards the centre of the water surface. When the laser has moved a distance `s=1m` or more (measured from curved face) from the lowest point in water, no light enters the gas. The refractive index of gas is `(mu_("water") = 4//3)`

Options

A. `4//sqrt(3)`
B. `sqrt(5)//2`
C. `2//sqrt(3)`
D. `sqrt(3)`

Answer

C

Explanation

Distance moved by laser `S=Rtheta`
`theta =(S)/(R )=(pi)/(3)`rad
If `sgt 1m` when no light enetrs the gas critical angle `c=theta`
`implies(1)/(sin60)=(mu_(W))/(mu_(G))=(2)/sqrt(3) therefore mu =(2)/sqrt(3)`