Conditions for obtaining an interference pattern of light are(A) Two…

The correct answer is Option (4) → (A), (C) and (D) only

A steady, clearly visible interference pattern needs a constant phase difference between the waves, a fringe width \( \beta = \lambda D/d \) large enough to be seen, and good contrast between bright and dark fringes.

(A) Two waves should be coherent — Correct. Only coherent waves keep a constant phase difference, so the bright and dark fringes stay in place.

(B) The distance of the screen from the slits should be small — Incorrect. Since \( \beta \propto D \), a small screen distance makes the fringes too narrow to see; the screen should be far away.

(C) The separation between slits should be small — Correct. Since \( \beta \propto 1/d \), a small slit separation gives fringes wide enough to be seen.

(D) Two coherent waves should have nearly the same amplitude — Correct. The minimum intensity is \( (a_1 - a_2)^{2} \), which is nearly zero only when \( a_1 \approx a_2 \); this gives dark fringes and good contrast.

Note: Statement (A) of this question is from the latest textbook (2026-27). Statements (B) and (C), on the screen distance and the slit separation, rest on the fringe width \( \beta = D\lambda/d \), which is printed only in the pre-rationalised textbook (2022-23). It was removed from the latest book, but the expression for fringe width is still in the CUET 2026 syllabus, so do not skip it.

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.”

NCERT (Pre-rationalised edition, 2022-23):
Interference of Light Waves and Young’s Experiment – “… Equations (10.18) and (10.19) show that dark and bright fringes are equally spaced and the distance between two consecutive bright and dark fringes is given by

    \( \displaystyle \beta = x_{n+1} - x_n \quad \text{or} \quad \beta = \frac{D\lambda}{d} \qquad (10.20) \)

which is the expression for the fringe width.”