Question

What happens, when the width of the slit aperture is increased in an experiment of single slit diffraction experiment :

• A. spread of diffraction region is increased
• B. spread of diffraction region is decreased
• C. spread of diffraction region will be decreased and mid-band becomes narrow
• D. none of the above

Answer 1

Answer: (C)

3

Answer 2

The phenomenon of single-slit diffraction describes how light spreads out after passing through a narrow opening. The extent of this spreading is characterized by the width of the central maximum in the diffraction pattern.

The condition for the minima in a single-slit diffraction pattern is given by:

$a \sin \theta = n \lambda$

where:

• $a$ is the width of the slit aperture
• $\theta$ is the angle of diffraction from the central axis
• $n$ is the order of the minimum (n = 1, 2, 3, ...)
• $\lambda$ is the wavelength of the light

For the first minimum (n=1), the angular position is given by:

$\sin \theta_1 = \frac{\lambda}{a}$

For small angles, $\sin \theta \approx \theta$. Therefore, the angular position of the first minimum is approximately:

$\theta_1 \approx \frac{\lambda}{a}$

The angular width of the central maximum (the "mid-band" or "spread of diffraction region") is the angle between the first minima on either side of the central axis. So, the angular width of the central maximum is $2\theta_1$.

Angular width of central maximum $\approx \frac{2\lambda}{a}$

From this relationship, it is clear that the angular width of the central maximum is inversely proportional to the width of the slit aperture ($a$).

If the width of the slit aperture ($a$) is increased:

1. The term $\frac{2\lambda}{a}$ will decrease. This means the angular width of the central maximum decreases.
2. A decrease in angular width implies that the "spread of the diffraction region is decreased".
3. Consequently, the central maximum (referred to as "mid-band") becomes narrower.

Therefore, option (3) provides the most complete and accurate description of what happens.

The angular width of the central maximum in a single-slit diffraction pattern is inversely proportional to the slit width ($a$). When the slit width ($a$) is increased, the angular width of the central maximum, which represents the spread of the diffraction region, decreases. Consequently, the central bright band (mid-band) becomes narrower.