Question

(a) Calculate the apparent depth of a black
point lying below a
cubical
and
transparent glass slab of side 4
centimeter. Where refractive-index of
glass is 1.6.​

Answer 1

Answer:

Apparent depth of the black point is 1.5 cm.

Explanation:

Let tₐ = apparent thickness/ depth

t = real thickness/depth

η = refractive index of slab w.r.t surrounding medium.

Given

$t = 4 \: cm$

$\eta = 1.6$

Formula

Apparent thickness/depth of glass stab is given by

$tₐ = t(1 - \frac{1}{ \eta} )$

Calculation

Substituting values of thickness and refractive index in the above equation, we get

$tₐ = 4(1 - \frac{1}{1.6} ) = 4(1 - \frac{10}{16} )$

$tₐ = 4(1 - \frac{5}{8} ) = 4 \times \frac{8 - 5}{8}$

$tₐ = 4 \times \frac{3}{8} = \frac{3}{2}$

$tₐ = 1.5 \: cm$