Question

To analyze the resulting pattern of bright and dark fringes when laser light passes through a single slit, what fundamental principle of light propagation is used?

Answer 1

To analyse the bright and dark fringes, the principle of interference of light waves is used in single slit diffraction experiment.

According to Huygens’s principle, every part of the wavefront in the slit emits wavelets. These are like rays that start out in phase and head in all directions. Each ray is perpendicular to the wavefront of a wavelet. Assuming the screen is very far away compared with the size of the slit, rays heading toward a common destination are nearly parallel. When they travel straight ahead, they remain in phase, and a central maximum is obtained. However, when rays travel at an angle(theta) relative to the original direction of the beam, each travels a different distance to a common location, and they can arrive in or out of phase. The ray from the bottom travels a distance of one wavelength (lambda) farther than the ray from the top. Thus a ray from the center travels a distance (lambda /2) farther than the one on the left, arrives out of phase, and interferes destructively. A ray from slightly above the center and one from slightly above the bottom will also cancel one another. In fact, each ray from the slit will have another to interfere destructively, and a minimum in intensity will occur at this angle. There will be another minimum at the same angle to the right of the incident direction of the light. Thus there will be a series of minima(dark fringes) and maxima(bright fringes) alternatively to the either side of the central bright fringe.