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 central peak of the diffraction pattern corresponds to the main lobe of the intensity distribution due to the diffraction effect. The number of interference peaks within the central diffraction peak is determined by the ratio of the width of the central diffraction peak to the fringe separation. The diffraction angle for the first minimum is given by: \[ \sin \theta = \frac{\lambda}{d} \] where \( \lambda = 450 \, nm} \) (wavelength of the monochromatic light) and \( d = 6 \, \mum} \) (distance between the slits). The interference fringes fall within the diffraction envelope, and the number of peaks of the interference fringes within the central diffraction peak is 6. Thus, the number of interference fringes within the central peak is 6.