Two coherent sources send light of wavelength 600 nm to a point P. The waves leave the sources in phase. The path difference between the two waves at P is 1.5 μm. The phase difference between the waves at P is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(5\pi\)
A path difference of one wavelength gives a phase difference of \( 2\pi \). So the phase difference is \( 2\pi \) times the number of wavelengths in the path difference.
\( \begin{aligned} \frac{\Delta x}{\lambda} &= \frac{1.5\times10^{-6}}{600\times10^{-9}} \\ &= 2.5 \end{aligned} \)
\( \begin{aligned} \phi &= 2\pi\times\frac{\Delta x}{\lambda} \\ &= 2\pi\times2.5 \\ &= 5\pi \end{aligned} \)
Hence, the phase difference at P is \( 5\pi \). The waves arrive out of phase, so P is a point of destructive interference.
NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “… where we have used the fact that a path difference of 2.5λ corresponds to a phase difference of 5π. The two displacements are now out of phase and the two displacements will cancel out to give zero intensity. …”