Diffraction-limited light beam

A diffraction-limited light beam refers to a beam of light that is limited in its ability to resolve fine details due to the phenomenon of diffraction. Diffraction occurs when light waves encounter an obstacle or aperture and spread out, causing interference patterns and blurring of the image.

Width of the beam at the source

The width of the beam at the source is given as 2r. This represents the diameter of the beam at its origin.

Falling on a screen at a distance D

The diffraction-limited light beam falls on a screen placed at a distance D from the source. The screen acts as a barrier that intercepts the beam and allows us to observe the resulting pattern.

Full-width of the spot illuminated on the screen

The full-width of the spot illuminated on the screen is the measure of the spread of the beam after passing through the aperture and reaching the screen. This full-width is given as a.

Relationship between wavelength, beam width, and distance

To determine the relationship between the wavelength (W), beam width (2r), and distance (D), we can consider the phenomenon of diffraction.

Diffraction occurs when a beam of light passes through an aperture or encounters an obstacle. The amount of diffraction that occurs depends on the wavelength of the light, the size of the aperture or obstacle, and the distance between the aperture or obstacle and the screen.

Diffraction formula

The diffraction formula that relates the full-width of the spot (a), wavelength (W), beam width (2r), and distance (D) is given by:

a = (W * D) / (2 * r)

Explanation of the formula

- The full-width of the spot (a) is directly proportional to the wavelength (W) and the distance (D).
- The full-width of the spot (a) is inversely proportional to the beam width (2r).

Therefore, the correct option is (a) DW/2r. This formula shows that the full-width of the spot illuminated on the screen is directly proportional to the wavelength and the distance, and inversely proportional to the beam width.