A small piece of wood is floating on the surface of a 2.5 m deep lake. Where does the shadow form on the bottom when the sun is just setting? Refractive index of water = 4/3

Explanation

Refer to the above given figure.
We can aaply Snell.s law for the refraction at the point S.
`upsilon sin theta=`constant
`implies " " 1x sin 60=(4)/(3)x sin theta`
`implies " " sin theta=(3)/(4)x sin 60=(3)/(4)x0.866=0.6495`
`implies " " theta=40.5^(@)`
Now length of the shadow can be written as follows : Length of shadow `=QT+TU`
`implies` Length of shadow `= RS +TU`
`implies` Length of shadow `= PR x "tan" 60^(@)+ST x "tan" 40.5`
`implies` Length of shadow `=1xx1.732+2x 0.854`
`implies` Length of shadow `=3.44 m.`