What is the relation between phase difference \( (\Delta \theta) \) and path difference \( (\Delta x) \)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \Delta\theta = \frac{2\pi}{\lambda}\,\Delta x \)
A path difference of one wavelength \( \lambda \) corresponds to a phase difference of \( 2\pi \) radians, and the phase difference is proportional to the path difference.
\( \displaystyle \frac{\Delta\theta}{2\pi} = \frac{\Delta x}{\lambda} \Rightarrow \Delta\theta = \frac{2\pi}{\lambda}\,\Delta x \)
The other options are not equivalent: Option (3) gives \( \Delta\theta \) the dimension of length squared, whereas a phase difference is a pure number; Option (2) inverts the dependence, so the path difference would fall as the phase difference rises; Option (4) has the wrong constant, since the correct form is \( \Delta x = \frac{\lambda}{2\pi}\,\Delta\theta \).
Note: A similar question was also asked in CUET (UG) 2022 on 17-08-2022 (Slot 2).