Question

The number of peaks of the interference fringes formed within the central peak of the envelope of the diffraction pattern will be:

• A. 2
• B. 3
• C. 4
• D. 6

Hint:

Remember that the number of interference fringes within the central diffraction maximum depends on the relative widths of the interference and diffraction patterns. The calculation often involves approximations unless exact dimensions are provided.

Answer 1

The Correct Option is D

The main lobe of the intensity distribution, resulting from diffraction, is represented by the central peak of the diffraction pattern. The quantity of interference peaks observed within this central diffraction peak is dictated by the quotient of the central diffraction peak's width and the fringe separation. The diffraction angle for the initial minimum is defined as: \[ \sin \theta = \frac{\lambda}{d} \] wherein \( \lambda = 450 \, nm} \) signifies the wavelength of the monochromatic light, and \( d = 6 \, \mum} \) represents the distance between the slits. The interference fringes are contained within the diffraction envelope. Specifically, there are 6 interference fringe peaks within the central diffraction peak. Consequently, the total count of interference fringes within the central peak is 6.