The diffraction pattern due to circular aperture consists of :a)a bright central disc surrounded by alternate dark and bright concentric rings with equal spacing between the ringsb)a bright central disc onlyc)a bright central disc surrounded by alternate dark and bright concentric ringsd)a dark central disc surrounded by alternate dark and bright concentric ringsCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Diffraction pattern due to circular aperture:

The diffraction pattern that occurs when light passes through a circular aperture is characterized by a bright central disc surrounded by alternate dark and bright concentric rings. This pattern is known as the Airy pattern or the Airy disk.

Explanation:

Huygens-Fresnel principle:
To understand the diffraction pattern, we need to consider the Huygens-Fresnel principle. According to this principle, every point on a wavefront acts as a source of secondary spherical wavelets. These wavelets interfere with each other to produce the overall diffraction pattern.

Diffraction of light:
When light passes through a circular aperture, it diffracts and spreads out. This spreading occurs due to the interference of the secondary wavelets generated by each point on the circular aperture.

Central disc:
The central disc in the diffraction pattern is bright because it corresponds to the constructive interference of the secondary wavelets that originate from the center of the circular aperture. The light waves from these wavelets add up in phase, resulting in a bright spot at the center.

Concentric rings:
The concentric rings in the diffraction pattern occur due to the interference of the secondary wavelets that originate from different points on the circular aperture. The distance between these points and the observation point determines the phase difference between the wavelets.

Constructive and destructive interference:
For certain points around the central disc, the secondary wavelets interfere constructively, resulting in bright rings. These bright rings occur when the path difference between the wavelets is an integral multiple of the wavelength of light.

On the other hand, for other points, the secondary wavelets interfere destructively, resulting in dark rings. These dark rings occur when the path difference between the wavelets is a half-integral multiple of the wavelength of light.

Equal spacing between the rings:
The spacing between the bright and dark rings in the diffraction pattern is equal. This is because the path difference between the wavelets changes uniformly with increasing distance from the center of the circular aperture. As a result, the bright and dark rings are evenly spaced.

Conclusion:
In summary, the diffraction pattern due to a circular aperture consists of a bright central disc surrounded by alternate dark and bright concentric rings. The bright rings occur due to constructive interference, while the dark rings occur due to destructive interference of the secondary wavelets. The spacing between the rings is equal, resulting in a visually appealing pattern known as the Airy pattern.

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