Two slabs of same thickness of 6 cm each are placed over one other as shown on table. Apparent depth of table surface is N cm. (N is nearest integer)

The correct answer is 6.

Analysis of the Image:
Based on the provided diagram, we have two slabs placed one on top of the other on a table surface:
1. The upper slab has a thickness of t₁ = 6 cm and a refractive index of μ₁ = 7/3.
2. The lower slab has a thickness of t₂ = 6 cm and a refractive index of μ₂ = 5/3.

Step-by-Step Derivation:
When viewing the table surface vertically from above the two slabs, the light rays pass through both media before entering the air. The apparent depth of the table surface from the top surface of the upper slab is given by the sum of the apparent depths through each medium:

$h_{\text{app}}=\frac{t_1}{{\mu }_1}+\frac{t_2}{{\mu }_2}$

Substitute the given values into the formula:

$h_{\text{app}}=\frac{6}{7/3}+\frac{6}{5/3}$

Simplify the fractions by multiplying the numerators by 3:

$h_{\text{app}}=\frac{18}{7}+\frac{18}{5}$

Calculate the decimal values for each term:

$\frac{18}{7}\approx 2.57\text{ cm}$

$\frac{18}{5}=3.6\text{ cm}$

Summing these values gives the total apparent depth:

$h_{\text{app}}=2.57+3.60=6.17\text{ cm}$

Rounding to the nearest integer N:
N = 6