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.
In this experiment, the slits S1 and S2 are a distance \(d\) apart. The screen is at a distance \(D\) from the slits, and light of wavelength \(\lambda\) is used. On the screen, the distance between the centre of a bright fringe and the centre of the next dark fringe is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{\lambda D}{2d}\)
For a point at a distance \( x \) from the centre of the screen, the path difference between the two waves is \( xd/D \). A bright fringe forms where this equals \( n\lambda \). A dark fringe forms where it equals \( (n+\frac{1}{2})\lambda \).
Take the bright fringe of order \( n \) and the dark fringe just after it:
\( \begin{aligned} x_{\text{bright}} &= \frac{n\lambda D}{d} \\ x_{\text{dark}} &= \left(n+\frac{1}{2}\right)\frac{\lambda D}{d} \\ x_{\text{dark}}-x_{\text{bright}} &= \frac{\lambda D}{2d} \end{aligned} \)
A dark fringe lies midway between two bright fringes. Hence, the distance from a bright fringe to the next dark fringe is \( \lambda D/2d \), half the fringe width.
NCERT (2026-27):
Interference of Light Waves and Young’s Experiment – “We will have constructive interference resulting in a bright region when \( xd/D=n\lambda \). That is,”
\( \displaystyle x=x_n=\frac{n\lambda D}{d} \)\( \displaystyle ;\ n=0,\pm1,\pm2,\ldots \qquad (10.13) \)
“On the other hand, we will have destructive interference resulting in a dark region when \( xd/D=\left(n+\frac{1}{2}\right)\lambda \) that is”
\( \displaystyle x=x_n=\left(n+\frac{1}{2}\right)\frac{\lambda D}{d} \)\( \displaystyle ;\ n=0,\pm1,\pm2 \qquad (10.14) \)