What is the apparent position of an object below a rectangular block of glass `6 cm` thick, if a layer of water `4 cm` thick is on the top of the glass ? Given `^(a)mu_(g) = 3//2 and ^(a)mu_(w) = 4//3`.

Explanation

Here, real depth of glass, `x_(1) = 6 cm`,
real depth of water, `x_(2) = 4 cm`.
`.^(a)mu_(g) = 3//2, .^(a)mu_(w) = 4//3`
If `y_(1),y_(2)` are the corresponding apparent depths,
Then, `(x_1)/(y_1) = .^(a)mu_(g) = (3)/(2)`
`:. y_(1) = (2)/(3) x_(1) = (2)/(3) xx 6 = 4 cm`
`(x_2)/(y_2) = .^(a)mu_(w) = (4)/(3)`
`:. y_2 = (3)/(4) x_2 = (3)/(4) xx 4 = 3cm`
Apparent position of the object
=`(y_1 + y_2) = (4 + 3) cm = 7 cm`
`:.` Rise in position of the object
=`(x_1 + x_2)-(y_1 + y_2) = (6 + 4) - (4 + 3)`
=`10 - 7 = 3 cm`.