Answer to Question #130442 in Optics for Emmanuel Ogana

Question

If the difference between the real depth and apparent depth of a swimming pool filled with water is 1.6m, determine the depth of the pool Assume refractive index of water is 1.33

Answer 1

$Real \space depth-Apparent\space depth=1.6$

$Apparent \space depth=\frac{real\space depth}{refractive\space index\space of\space water}$

Assume that apparent depth= x therefore, real depth= apparent depth(x)+1.6

substituting this in the above equation

$x=\frac{x+1.6}{1.33}$

$1.33x-x=1.6$

$0.33x=1.6$

$x=4.848$

Therefore Apparent depth=$4.848$

The real depth of the pool is therefore $4.848+1.6=6.448m$

Answer= 6.448m