Assertion (A): In the interference pattern of two coherent point sources of equal intensity \( I_0 \), every maximum has the same intensity \( 4I_0 \).
Reason (R): In the diffraction pattern of a single slit, different maxima have different intensities.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
Assertion (A) In the interference pattern of two coherent point sources of equal intensity \( I_0 \), every maximum has the same intensity \( 4I_0 \). — True. At every point where the path difference is \( n\lambda \), the two waves of equal amplitude \( a \) arrive in phase. The resultant amplitude is \( 2a \), so the intensity is \( 4I_0 \) for every value of \( n \).
Reason (R) In the diffraction pattern of a single slit, different maxima have different intensities. — True. The central maximum at \( \theta=0 \) is the brightest, and the secondary maxima on either side go on becoming weaker as their order increases.
Why R does not explain A?
(R) describes a different pattern, the diffraction pattern of a single slit, and says nothing about the waves from two point sources.
(A) follows from constructive interference of two waves of equal amplitude. For a path difference \( n\lambda \) the amplitude is \( 2a \) whatever \( n \) is. So every maximum has the intensity \( 4I_0 \). Hence (R) is not the correct explanation of (A).
NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “To summarise: If we have two coherent sources S1 and S2 vibrating in phase, then for an arbitrary point P whenever the path difference,
\( S_1P\sim S_2P=n\lambda\quad(n=0,1,2,3,\ldots) \qquad (10.9) \)
we will have constructive interference and the resultant intensity will be 4I0; the sign ~ between S1P and S2P represents the difference between S1P and S2P.”
The Single Slit – “It is observed that the intensity has a central maximum at \( \theta=0 \) and other secondary maxima at \( \theta\approx(n+1/2)\,\lambda/a \), which go on becoming weaker and weaker with increasing n.”