In a beaker partly filled with water, the depth of water seems to be 9cm. On pouring more water in it, the real depth of water is increased by 4cm. Now the apparent depth of water seems to be 12 cm. Determine the refractive index of water and initial depth of water in the beaker.

Explanation

Let the refractive index of water be `mu` and initial depth of water in the beaker be x.
`therefore " " mu = (x)/(9) or, x = 9 mu`.
When more water is poured in the beaker, the real depth of water becomes `(x + 4)cm`.
`therefore "In te second case", mu = (x+4)/(12)`
`or, " " 12mu = x + 4 or, 12mu = 9mu + 4 or, 3mu = 4`
`therefore " " mu = (4)/(3) = 1.33`
`therefore " " "Intial depth of water in the beaker",`
`x = 9mu = 9 xx(4)/(3) = 12cm`