Question

A postage stamp placed under a glass slab of refractive index 1.5, appears raised by 0.8 mm. What is the thickness of glass slab.

Answer 1

Given:

Refractive Index of glass (\(\mu \)) = \(1.5\)

Apparent Shift (\(s\)) = \(0.8\text{ mm}\)

The formula relating thickness \((t\)), refractive index \((\mu\)), and apparent shift \(s\) is:

\[ \text{Apparent Shift } (s) = t \times \left( 1 - \frac{1}{\mu} \right) \]

\[ 0.8 = t \times \left( 1 - \frac{1}{1.5} \right) \]

Convert 1.5 into a fraction \(\left( \dfrac{3}{2} \right)\):

\[ 0.8 = t \times \left( 1 - \frac{2}{3} \right) \]

\[ 0.8 = t \times \left( \frac{1}{3} \right) \]

\[ t = 0.8 \times 3 \]

\[ t = 2.4 \ \text{mm} \]