A pile driven into the bottom of a lake extends `3m` above the bottom of a lake and `1m` above the surface of water `(._amu_omega)=4//3`. If the sun is `30^@` above the horizon, then the length of the shadow of the pile on the bottom is approximately

Options

A. `1.73m`
B. `2.73m`
C. `3.00m`
D. `3.46m`

Answer

D

Explanation

In `DeltaABP`, `tan60^@=(BP)/(1)impliesBP=sqrt3m`
Refraction at air-water surface:
`1xxsin60^@=._amu_omegasinr`
`sqrt3/2=4/3sinr`
`sinr=(3sqrt3)/(8), cos r=sqrt(1-((3sqrt3)/(8))^2)=(sqrt(37))/(8)`
`tan r=(sinr)/(cosr)=(3sqrt3)/(sqrt37)`
In `DeltaPQR`,
`tanr=(QR)/(PQ)`
`(3sqrt3)/(sqrt37)=(QR)/(2)`
`QR=(6sqrt3)/(sqrt37)=sqrt3`
Total length of image `=BP+QR=2sqrt3=3.46m`