An air bubble in a glass slab with refractive index `1.5` (near normal incidence) is `5 cm` deep when viewed from one surface and `3cm` deep when viewed from the opposite face. The thickness (in `cm)` of the slab is

Options

A. 12
B. 16
C. 8
D. 10

Answer

A

Explanation

Suppose that the air bubble (P) is at a distance x from the face A and t = thickness of the slab.
`mu = ("Real depth")/("Apparent depth ")`
`therefore` Apparent depth = `("Real depth")/(mu)`
When the air bubble (P) is seen from the face A ,
`A.D. = (R.D.)/(mu) therefore 5 = (x)/(mu) " " ... (1)`
From the side `B 3 = (t - x)/(mu) " " ... (2)`
`therefore 5 + 3 = (x)/(mu) + (t- x)/(mu) = (t)/(mu)`
`therefore t = 8 mu = 8 xx 1.5 = 12` cm