Read the passage and answer the question.
If we look closely at the shadow of an opaque object, we see alternate dark and bright regions near the edge of the geometrical shadow. This happens because of a particular phenomenon. All types of waves show it, be it sound waves, light waves, water waves or matter waves.
In a single-slit experiment, the slit width is made three times. What happens to the width of the central maximum?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → It becomes one-third
In single-slit diffraction, the central maximum spreads between the first minima on the two sides, at \( \theta=\pm\lambda/a \). On a screen at a distance \( D \), its width is
\( \begin{aligned} \beta_0 &= \frac{2\lambda D}{a} \end{aligned} \)
With the new slit width \( a'=3a \),
\( \begin{aligned} \beta_0' &= \frac{2\lambda D}{a'} \\ &= \frac{2\lambda D}{3a} \\ &= \frac{\beta_0}{3} \end{aligned} \)
From the above, \( \beta_0'=\beta_0/3 \). Hence, a wider slit gives a narrower central maximum, one-third of the old width.
NCERT (2026-27):
The single slit – “It is observed that the intensity has a central maximum at θ = 0 … The minima (zero intensity) are at \( \theta \approx n\lambda/a \), n = ±1, ±2, ±3, ....”