Question

At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is

• A. $ \pi radian $
• B. $ \frac{\pi}{8} radian $
• C. $ \frac{\pi}{4} radian $
• D. $ \frac{\pi}{2} radian $

Answer 1

The Correct Option is A

To solve this problem, we need to understand the concept of single-slit diffraction and the phase difference at the point of the first minimum adjacent to the central maximum.

In a single-slit diffraction pattern, the first minimum occurs when the path difference between the light from the edge of the slit and that from the midpoint of the slit is half a wavelength. This occurs at the angle where the path difference is \frac{\lambda}{2} , where \lambda is the wavelength of the light.

Now, for a slit of width a illuminated by monochromatic light of wavelength \lambda , the condition for the first minimum in the diffraction pattern is given by:

a \sin \theta = \frac{\lambda}{2}

This condition implies that the light from the center of the slit to the edge is out of phase by \pi radian (since a path difference of half a wavelength corresponds to a phase difference of \pi radian ).

Hence, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint at the first minimum is:

Correct Answer: \pi radian

Let's summarize why the other options are incorrect:

• The options \frac{\pi}{8} radian , \frac{\pi}{4} radian , and \frac{\pi}{2} radian do not correspond to the condition for the first minimum in diffraction, which is specifically \pi radian due to the half-wavelength out-of-phase condition.

Understanding this helps in solving similar problems where the concept of path and phase differences in diffraction patterns are important.