Question

Angular width of ntral maximum of a diffraction pattern due to a single slit does not depend upon

• A. Distance between slit and source
• B. Wavelength of light used
• C. Width of the slit
• D. Frequency of light used

Hint:

Diffraction Key Point: Angular width of central maximum in single-slit diffraction: \[ \theta = \frac\lambdaa, \quad \textAngular width = 2\theta \] Depends on $\lambda$, $a$, and $f$ (indirectly via $\lambda$). It does not depend on the distance from slit to source.

Answer 1

The Correct Option is A

In single-slit Fraunhofer diffraction, the angular position $\theta$ of the first minimum is given by: \[ a \sin\theta = \lambda \] where $a$ is the width of the slit and $\lambda$ is the wavelength of the incident light. The angular width of the central maximum is defined as $2\theta$ (from $-\theta$ to $+\theta$), and for small $\theta$, it approximates to: \[ 2\theta \approx \frac{2\lambda}{a} \] Hence, the angular width depends directly on the wavelength and inversely on slit width. Since $\lambda = \frac{v}{f}$, it also depends on frequency. However, it does not depend on the distance between slit and source, assuming Fraunhofer conditions (plane wave approximation).

Answer 2

Step 1: Understanding Diffraction and Angular Width
Diffraction occurs when waves, such as light waves, encounter an obstacle or slit and bend around it. In a single slit diffraction pattern, a central bright fringe (central maximum) appears, surrounded by alternating dark and bright fringes. The angular width of the central maximum is the angle between the first minima on either side of the central bright fringe.

Step 2: Formula for Angular Width of Central Maximum
The angular width (θ) of the central maximum in single slit diffraction is given by:
θ = 2λ / a
where λ is the wavelength of the light used, and a is the width of the slit.

Step 3: Parameters Affecting Angular Width
From the formula, angular width depends on:
- The wavelength (λ) of the light source
- The slit width (a)
It does not depend on the distance between the slit and the screen or the source.

Step 4: Why Distance Between Slit and Source Does Not Affect Angular Width
Changing the distance between the slit and the source changes the intensity or brightness of the light reaching the slit but does not alter the wavelength or slit width. Since angular width depends only on λ and a, this distance has no effect on the angular width of the central maximum.

Step 5: Conclusion
Therefore, the angular width of the central maximum in a single slit diffraction pattern does not depend on the distance between the slit and the source.