Question

The width of the central maximum of a diffraction pattern on a single slit does not depend upon

• A. frequency of light used
• B. width of the slit
• C. distance between slit and source
• D. wavelength of light used

Hint:

Be careful not to mix up the two distances in a diffraction setup! The distance $D$ that alters the pattern is the distance from the slit to the screen. The distance from the source to the slit is irrelevant because optical elements (like collimating lenses) are used to make the incoming light rays parallel before they reach the slit.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks us to identify which physical parameters do not influence the linear width of the central bright maximum in a standard single-slit Fraunhofer diffraction experiment.

Step 2: Key Formula or Approach:
The total linear width ($W$) of the central maximum on a projection screen is given by the single-slit diffraction formula: $$W = \frac{2\lambda D}{a}$$ Where: $\lambda$ is the wavelength of the light source $D$ is the distance between the slit and the observation screen $a$ is the width of the slit aperture width itself.

Step 3: Detailed Explanation:
Let's analyze the dependencies using our formula: Wavelength ($\lambda$): The width $W$ is directly proportional to $\lambda$. Thus, it depends on option (D). Frequency ($f$): Since the speed of light is $c = f\lambda \implies \lambda = \frac{c}{f}$, the width can be rewritten as $W = \frac{2cD}{af}$. Thus, it depends on the frequency of light, option (A). Slit width ($a$): The width $W$ is inversely proportional to $a$. Thus, it depends on option (B). Distance between slit and source: The wave front hitting the slit is assumed to be a plane wave (Fraunhofer setup). The distance between the slit and the original light source has no bearing on the diffraction divergence spreading beyond the slit aperture. Therefore, the width of the central maximum is completely independent of the distance between the slit and the source.

Step 4: Final Answer:
The width does not depend on the distance between the slit and the source, which corresponds to option (C).