Choose the correct relation between phase difference ( Δφ ) and Path…

The correct answer is Option (2) → \( \Delta\phi = \displaystyle\frac{2\pi}{\lambda}\,\Delta x \)

A wave repeats itself after travelling one wavelength, and in that distance its phase changes by \( 2\pi \). So a path difference \( \Delta x \) corresponds to the same fraction of \( 2\pi \) as \( \Delta x \) is of \( \lambda \):

    \( \displaystyle \frac{\Delta\phi}{2\pi} = \frac{\Delta x}{\lambda} \)

    \( \displaystyle \Delta\phi = \frac{2\pi}{\lambda}\,\Delta x \)

For example, a path difference of \( \lambda/2 \) gives a phase difference of \( \pi \).

Note: A similar question was also asked in CUET (UG) 2023 on 11-06-2023 (Slot 3).

NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “… Thus, if the displacement produced by S₁ is given by

    \( \displaystyle y_1 = a \cos \omega t \)

then the displacement produced by S₂ will be given by

    \( \displaystyle y_2 = a \cos (\omega t - 4\pi) = a \cos \omega t \)

where we have used the fact that a path difference of 2λ corresponds to a phase difference of 4π.”