Identify the INCORRECT statement(s) in the context of phenomenon of interference.
(A) All bright and dark fringes have equal width.
(B) All bright fringes have the same intensity.
(C) Fringe width depends on the distance of screen from the slits.
(D) All dark and bright fringes are not equally spaced.
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (D) only
In Young's double-slit experiment the bright and the dark fringes are equally spaced, with fringe width
\( \displaystyle \beta = \frac{\lambda D}{d} \)
where \( D \) is the slit-screen distance and \( d \) the slit separation.
(A) All bright and dark fringes have equal width. — Correct statement. Every bright and every dark fringe has the same width \( \beta = \lambda D/d \).
(B) All bright fringes have the same intensity. — Correct statement. In the double-slit pattern the intensity is \( I = 4I_0\cos^{2}(\phi/2) \), so every bright fringe has the same maximum intensity \( 4I_0 \).
(C) Fringe width depends on the distance of screen from the slits. — Correct statement. \( \beta \propto D \).
(D) All dark and bright fringes are not equally spaced. — Incorrect statement. The fringes are equally spaced, one fringe width \( \beta \) apart throughout the pattern.
NCERT (2026-27):
Interference of Light Waves and Young’s Experiment – “… We will have constructive interference resulting in a bright region when \( \frac{xd}{D} = n\lambda \). That is,
\( \displaystyle x = x_n = n\frac{D\lambda}{d}; \quad n = 0, \pm 1, \pm 2, \ldots \qquad (10.13) \)”
Interference of Light Waves and Young’s Experiment – “… Thus dark and bright bands appear on the screen, as shown in Fig. 10.13. Such bands are called fringes. Equations (10.13) and (10.14) show that dark and bright fringes are equally spaced.”