Case: Read the passage and answer the question.
YDSE is the abbreviation used for Young’s double-slit experiment, which shows the interference of light. Interference of light is the phenomenon in which two light waves meet each other while travelling in the same medium. A light source is kept behind a wall in which two slits, S1 and S2, are made. On the screen there appears a pattern of alternate bright and dark fringes. The central fringe is always bright.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In this experiment, the intensity is zero at a point on the screen where the path difference between the waves from S1 and S2 is \(2.5\lambda\).
Reason (R): A path difference of \(2.5\lambda\) corresponds to a phase difference of \(5\pi\), so the two waves reach that point out of phase.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both (A) and (R) are correct and (R) is the correct explanation of (A).
Assertion (A) In this experiment, the intensity is zero at a point on the screen where the path difference between the waves from S1 and S2 is \(2.5\lambda\). — True. The waves from the two slits come from the same source and have equal amplitudes. At this point they meet with opposite displacements, so the resultant displacement is zero.
Reason (R) A path difference of \(2.5\lambda\) corresponds to a phase difference of \(5\pi\), so the two waves reach that point out of phase. — True. A path difference of one wavelength gives a phase difference of \( 2\pi \), so \( 2.5\lambda \) gives \( 2.5\times2\pi=5\pi \).
Why Reason (R) explains Assertion (A)?
If the wave from S1 gives \( y_1=a\cos\omega t \), the wave from S2 gives \( y_2=a\cos(\omega t+5\pi) \). This is the same as \( -a\cos\omega t \).
The sum \( y_1+y_2 \) is zero at every instant. This is destructive interference, and the intensity at that point is zero.
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. This is referred to as destructive interference.”