To demonstrate the phenomenon of interference, we require two sources, which emit radiation of
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → the same frequency and having definite phase relationship
Interference gives a steady pattern of bright and dark fringes only when the two sources are coherent: the phase difference between them must stay constant in time, which needs the same frequency and a definite phase relationship.
Option (1) nearly the same frequency — Incorrect. If the frequencies differ even slightly, the phase difference keeps changing and the fringes wash out.
Option (2) the same frequency — Incorrect. The same frequency is necessary but not enough; the phase difference between the sources must also stay fixed.
Option (3) different wavelength — Incorrect. Different wavelengths mean different frequencies, so the phase difference varies with time and no steady pattern forms.
Option (4) the same frequency and having definite phase relationship — Correct. The same frequency with a definite phase relationship makes the sources coherent.
NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “… Now if the two sources are coherent (i.e., if the two needles are going up and down regularly) then the phase difference \( \phi \) at any point will not change with time and we will have a stable interference pattern; i.e., the positions of maxima and minima will not change with time.”
Summary – “… But this term is important only if it has a non-zero average, which occurs only if the sources have the same frequency and a stable phase difference.”