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प्रश्न
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.
संख्यात्मक
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उत्तर
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 \(\left( \dfrac{3}{2} \right)\):
\[ 0.8 = t \times \left( 1 - \frac{2}{3} \right) \]
\[ 0.8 = t \times \left( \frac{1}{3} \right) \]
\[ t = 0.8 \times 3 \]
\[ t = 2.4 \ \text{mm} \]
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