Diffraction

Diffraction in sound waves and radio waves are readings observed as they have a relatively longer wavelength compared to light waves.

$Diffraction in sound waves and radio waves$

In the above figure l << a, when the light (plane) waves pass through the slit and the barrier forms a sharp shadow. As the slit 'a' is made smaller, light falls out into the formerly shadow region. This enrichment of light into the geometric shadow region is called diffraction. Note that 'a' is the transverse dimension of the slit and the effect of diffraction can be ignored if the ration of a/l is large. In such a case, light appears to be trained in straight line paths and is represented as rays. Thus, 'Ray', or 'geometrical optic' as it is called, is actually a limiting case of wave optics or physical optics.

Sub Topics

Diffraction of Light at a Single Slit
Note on diffraction:

Diffraction of Light at a Single Slit

$diffraction of light at a single slit$

Consider a parallel beam of light from a lens falling on a slit AB. As diffraction occurs, the pattern is focused on the screen XY with the help of lens L₂

.Each point on the unblocked portion of plane wavefront AB sends out secondary wavelets in all directions. The waves from points equidistant from the center C lying on the upper and lower half reach the point O with path difference being zero and hence reinforce each other producing a maximum intensity at the point 0.

Consider a point 'P' on the screen. The intensity at P will depend on the path difference between the secondary waves emitted from the corresponding point of the wavefront. Consider a set of waves making an angle q with CO. Draw AN perpendicular to BK. The path difference between the secondary waves reaching P from

A and B = BN = AB Sin q = a sin q

where AB = a width of the aperture.

If BN = a (i.e., path difference) the whole wave front can be considered to be divided into two halves, i.e., CA and CB. The path difference between A and C will be l/2 and so for every point in the upper half AC, there is a corresponding point in the lower half CB for which the path difference between the waves is l/2. So P is a point of destructive interference.

Path difference = asin θ_n = nλ

sin θ_n = nλ

q_n is the angle of diffraction of nth dark fringe from O.

Note on diffraction:

Diffraction occurs due to interference of two wave trains coming from two different points of the same wavefront and so a special case of interference occurs. Also the width and intensities of fringes in a diffraction is different and not equally bright. In interference, width and intensities of fringes are all equal.