Question

A path length of 1m in air is equal to a path length of \(x\) m in a medium of refractive index 1.5. Then the value of \(x\) (in meters) is:

• A. 1
• B. \(\frac{3}{5}\)
• C. \(\frac{5}{3}\)
• D. \(\frac{2}{3}\)
• E. \(\frac{1}{2}\)

Hint:

Optical path length is a concept used in optics to account for the effect of a medium on the propagation of light.

Answer 1

The Correct Option is D

The optical path length \( L \) is given by \( L = n \cdot s \), where \( n \) is the refractive index and \( s \) is the actual path length. For air (with \( n = 1 \)) and the medium (with \( n = 1.5 \)): \[ L_{{air}} = 1 \cdot 1\, {m} = 1\, {m} \] \[ L_{{medium}} = 1.5 \cdot x\, {m} = 1\, {m} \implies x = \frac{1}{1.5} = \frac{2}{3}\, {m} \]