Diffraction was first observed by Francesco Grimaldi in 1665. He noticed that light waves spread out when made to pass through a slit. Later it was observed that diffraction not only occurs in small slits or holes but in every case where light waves bend round a corner.
One of the most common examples of difraction in nature is the tiny specks or hair-like transparent structures, known as "floaters" that we can see when we look up at the sky. This illusion is produced within the eye-ball, when light passes through tiny bits in the vitreous humour. They are more prominently observed when one half-closes his eyes and peeps through them.
The phenomenon of diffraction can be readily explained using Huygens' principle:
When the wavefront of a light ray is partially obstructed, only those wavelets which belong to the exposed parts superpose, in such a way that the resulting wavefront has a different shape. This permits bending of light around the edges. Colourful fringe patterns are observed on a screen due to diffraction.
In the early 1800s, most of the people who wrote and submitted papers on diffraction of light were believers of the wave-theory of light. However, their views contradicted those of Newton's supporters' and their would be regular discussions between these two sides. One such person, who believed in the wave theory was Augustin Fresnel, whoin 1819, handed a paper to the French Academy of Sciences, about the phenomenon of diffraction. However, the Academy mainly consisting of Newton's supporters, tried to challenge Fresnel's point of view by saying that if light was indeed a wave, these waves, which were diffracted from the edges of a sphere, would cause a bright area to occur within the shadow of the sphere. This was indeed oberved later, and the area is today known as the Fresnel Bright Spot.
Diffraction by a single slit
Let us assume a slit of width d at which a parallel beam of light consisting of light rays of wavelength λ, is incident (refer to diagram). According to Huygens' principle each particle that is reached by the wavefronts of these waves becomes a source of secondary wavelets. These secondary wavelets are made to pass through a convex lens, at whose focal point, there is a screen. The point P0 on the screen is the intersection of the bisector of the plane of the slit and the plane of the screen, and receives waves which travel the same distance, and hence are in phase. Therefore, a constructive interference occurs at P0, and a bright spot is observed. Another point P on the screen, receives all the waves which are diffracted by an angle θ.
A perpendicular from point A, the tip of the slit is dropped onto the waves which reach P to represents the wavefronts of these waves. Hence, by simple trigonometry, the optical path difference between a wave emitted by A and one emitted by the centre of the slit is
(d/2) sin θ
A particular angle is considered, for which
(d/2) sin θ = λ/2
These two waves have a phase difference, which is given by
δ = (2π/λ)(λ/2) = π
Hence they will cancel each other out, thus producing a dark fringe.
Therefore, dsin θ = λ is the condition for the first dark fringe. It can then be concluded that dark fringes are observed when
dsin θ = nλ, where n is an integer.
Similarly, bright fringes will be observed for the cases when
dsin θ = (n + 1/2)λ, where n is an integer.
Intensity of brightness on the screen
The amplitude EP of the electric field at P, when calculated is found to be equal to E0((sin β) / β) where,
β = ( π/λ ) dsin θ
and E0 is the amplitude at the point P0, which corresponds to θ=0.
Since the intensity is directly proportional to the square of amplitude,
I =I0 ((sin2 β) / β2)
Hence a graph showing the variation of intensity as a function of sin β can be plotted.
Diffraction by a circular aperture
When a parallel beam of light is incident on an opaque surface with a pin-hole (refer to diagram), the light is diffracted by the hole. When a screen is placed at a considerable distance from the surface, alternate light and dark rings of decreasing intensity are observed. As the wavefronts of the incident light rays reach the points of the hole, they emit secondary wavelets in all directions, according to Huygens' principle, which interfere to produce the light and dark rings. It can be calculated that the first dark ring is formed by the light diffracted from the hole at an angle θ, such that
sin θ ≈ (1.22λ)/s
where λ is the wavlength of the incident light and s is the diameter of the pin-hole, such that s << d, d being the perpendicular distance from the screen to the hole. Also, the radius of the first dark ring is given by
R ≈ (1.228d)/s.
If however, the diffracted light is converged with a convex lens onto a screen placed at its focal length, f, radius of the first dark ring will be
R = (1.22λf)/s
This radius is known as the "radius of the diffraction disc".
It can also be proved from the above results that it is not possible to converge the light emitted by a point source to a point on the screen with the help of a convex lens. The bright disc formed on the screen is konwn as the image disc.
Diffraction due to a straight edge
Let S be a point source of light emitting spherical wavefronts which are intercepted by an opaque object with a sharp edge A (refer to diagram). The light is then collected on a screen which is placed behind the opaque object. According to Huygens' principle, the edge on being reached by the incident light, becomes a source of secondary wavelets, which interfere with the light waves to produce a variation pattern on the screen. A point P0 is marked, which is the intersection of the line passing through S and A, and the screen. A graph can then be plotted, showing the variation of intensity as a function of distance from the point P0. It can also be conculded from the graph that the difference between the maximum and minimum intensity areas goes on decreasing as the distance from P0 increases, till we finally get uniform illumination on the screen.
One of the most useful instruments used in the study of light are the diffraction gratings. A diffraction grating has a number of close slits, known as rulings, whose thickness is of the order of wavelength of light. Light which passes through them forms narrow interference fringes. Even an opaque surface with narrow parallel grooves can be used as a diffraction grating, but light in this case, is scattered back from the grooves. As the number of slits in a diffraction grating is increased, the pattern obained on the screen becomes more and more complicated as compared. The bright fringes narrow down and the fringe width of dark areas increases.
Diffraction gratings are widely used in measuring the wavelength of light (by measuring the width of the interference fringes caused due to diffraction from the narrow slits of the diffraciton grating), emitted by sources like lamps or stars. Special diffraction spectroscopes make use of diffraction gratings for this purpose.
The dispersion of a diffraction grating is expressed as
D = Δθ/Δλ = m/(d cosθ)
where Δθ is the angular separation of two lines, whose wavelengths differ by Δλ in the first expression. To achieve a high dispersion, we have to work on a small grating spacing, d, but large values of m.
The resolving power of a grating can be expressed as:
R = λav/Δλ = Nm
where λav is the mean spectrum of two close spectral lines and is the wavelength difference between them in the first expression. To achieve a high resolving power, we muct have a high number of rulings, N.
