A surveryor on one bank of canal observed the image of the 4inch and 17ft marks on a vertical staff,which is partially immersed in the water and held against the bank directly opposite to him, coincides If the `17ft`mark and the suveryor's eye are both `6ft`above the water level ,estimate the width of the canal ,assuming that the reflective index of the water is`4//3`.Zero mark is at the bottom of the canal.

Answer

`16`feet

Explanation

Let width of canal is `'d'`image of `17`ft .mark will be formed by partial reflection and image of `4`inch mark will be formed by partial refraction
`DeltaOMN`:
`sinbeta=(d//2)/(sqrt((d//2)^(2)+(32//3)^(2)))………..(1)`
`sinalpha=(d//2)/(sqrt((d//2)^(2)+(6)^(2)))………..(2)`
from shell's law `rArr(4)/(3)sinbeta=1sinalpha`
from (1)and(2) `rArr (4)/(3)xx(d//2)/(sqrt((d//2)^(2)+(6)^(2)))=1xx(d//2)/(sqrt((d//2)^(2)+(6)^(2))) rArr d=16ft`
`d=16ft`