The document discusses the phenomenon of diffraction, including its historical discovery and the principles underlying light wave behavior according to Huygen's theory. It distinguishes between Fresnel and Fraunhofer diffraction, detailing their conditions and effects such as principal and secondary maxima. Additionally, it explains the resolving power of optical instruments and the applications of diffraction gratings in spectroscopy and holography.

1. Diffraction

2. Introduction
• The phenomenon of diffraction was first discovered by
Grimaldi in 1665.
• Bending of light around the edge of an obstacle is called
diffraction.
Sound waves bend round objects of a similar
size to their wavelength. The wall has a similar
size to the sound's wavelength. The effect is
called diffraction.
Sound
Light has a very small wavelength. So only very
small objects or gaps can affect its direction.
The wall blocks the light and the person can't
see round the corner.

3. Huygen’s Principle
• Huygen postulated a model for light waves, similar to water
waves. On the basis of this model, he proposed a hypothesis
for geometrically constructing the position of a wavefront.
• Postulate 1:
Each point on a wavefront (primary wavefront) acts as a source
of new disturbances, called secondary wavelets, which travel in
all directions with the velocity of light in that medium.
• Postulate 2:
The surface touching these secondary wavelets tangentially in
the forward direction at any instant gives a new wavefront, called
a secondary wavefront at that instant.

4. Construction of Secondary Wavefronts
• Huygen postulated that the action of
the secondary wavelets was confined
only to the points at which they
touched the forward envelope, and
thus no backward wavefront exists.
• According to Stoke’s law, the intensity
of the spherical wavelets varies as
where θ is the angle between the
direction of propagation of the wavelet
and the normal at that point. For
backward direction, θ =180°; therefore,
intensity = 0.
Construction of secondary
wavefront

5. Phenomenon of Diffraction
• Diffraction of light is the phenomenon of bending of light waves
around the corners of an obstacle or an aperture placed in its path,
and their spreading into the region of the geometrical shadow.
• Diffraction becomes significant when the dimensions of the
aperture or obstacle are comparable to the wavelength of the light.
• It occurs due to mutual interference of the secondary wavelets
starting from portions of the primary wavefront, which are allowed
to pass through the aperture.

6. Difference between Interference and
Diffraction Fringes

7. Types of Diffraction
• Fresnel diffraction occurs when the source and the screen
are at a finite distance from the diffracting aperture, such that
the incident and diffracted wavefronts are spherical or
cylindrical.
• Fraunhofer diffraction occurs when the source and the
screen are at an infinitely large distance from the diffracting
aperture, such that incident and diffracted wavefronts are
plane.

8. Resultant of Multiple Simple Harmonic Motions
• Let us assume that a particle is simultaneously acted upon by n SHM
vibrations. All the vibrations have the same amplitude A, and δ
represents the phase difference between successive vibrations.
• A phase difference δ exists between bc and ab, bc and cd, etc. The
phase difference between cd and ab is 2δ, between de and ab is 3δ,
etc.
• Here, Resultant R can be given by
Resultant of multiple SHMs

9. Fraunhofer Diffraction at Single Slit
• If the source and the screen are at infinitely large distances from the
diffracting aperture, both the incident and the diffracted wavefronts can
then be assumed to be plane wavefronts. The resulting diffraction is
called Fraunhofer diffraction.
• The phase difference δ between waves originating from any two
consecutive parts is expressed as
• The expression for intensity can
be written as
Schematic of single-slit diffraction

10. Fraunhofer Diffraction at Single Slit
 Principal Maxima
The resultant R can be written as
R will maximize to AT for =0, that is,
Thus,  = 0 or the secondary wavelets that travel normal to the slit result in
maxima on the screen. These are known as the principal maxima.
 Position for Minimum Intensity
• The intensity on the screen would be minimum if sin=0.

11. Fraunhofer Diffraction at Single Slit
 Secondary Maxima
• In addition to the principal maxima for  = 0, weak secondary
maxima are also observed between equally spaced minima.
• Intensity of the first and second secondary maximum can be
given by I1 and I2 respectively,
• ;
• Intensity of the principal maxima can be given by
• Thus, the intensity of secondary maxima decreases
progressively and most of the incident light energy is
concentrated in the principal maxima.

12. Fraunhofer Diffraction at Single Slit
• The principal maximum is at ɸ = 0 and the secondary maxima
occur at and so on.
• Minima positions that lie between secondary maxima are given
as ɸ =±π, ±2π, ±3π, and so on.
• Thus, the secondary maxima are not exactly midway between
two minima but are displaced towards the centre of the
diffraction pattern.
Schematic representation
of variation of intensity
versus ɸ

13. Fraunhofer Diffraction at Double Slit
• Now consider the diffraction
pattern obtained from an
arrangement having two slits, each
having a width ‘d’ and separated by
a distance ‘a’.
• The resulting fringe pattern will
then consist of the interference
pattern due to the two slits. Each
individual slit will also produce a
diffraction pattern.
• PD between the two interfering
waves is
Path difference between
interfering waves

14. Fraunhofer Diffraction at Double Slit
• The total intensity of the fringe pattern can be given by
• The first term of above equation is called the interference
factor and the second term is called the diffraction factor.
• If the zero of diffraction envelope
coincides with a maxima of
interference pattern, we see no
intensity on the screen. This order
of interference pattern is, therefore,
missing and is called the missing
order.
Double-slit diffraction pattern with
interference

15. N-slit Diffraction or Plane Diffraction Grating
• Plane Transmission Grating In this gratings are constructed using ruling
of equidistant parallel lines on a transparent material like glass using a
fine diamond point. The ruled lines are opaque to light, whereas the
space between any two lines is transparent to light and act as slits.
• Plane or Concave Reflection Gratings Another method of producing
gratings is by drawing lines on a plane or a concave silvered surface.
Light then gets reflected from a point situated between two lines.
Diffraction due to
plane grating

16. Resolving Power
• The ability of an optical instrument to form two separate
diffraction patterns of two objects is called its resolving power.
• A criterion for resolution of two point sources by an optical
instrument was first proposed by Rayleigh.
According to the Rayleigh’s criterion, two point sources
are resolvable by an optical instrument if the central
maximum of the diffraction pattern of one of them falls
over the first minimum of the diffraction pattern of the
other.
• Similarly, two spectral lines are resolvable if the central
maximum of the diffraction pattern of one of the wavelengths
falls over the first minimum due to the other wavelength, or
vice versa.

17. Resolving Power
Schematic representation of Rayleigh’s criterion (a) Widely separated wavelengths (b)
Resultant showing dip (c) Very close wavelengths

18. Resolving Power of Grating
• The ability of a grating to form separate diffraction
maxima for two very close wavelengths and thereby to
resolve the two wavelengths is called the resolving power
of the grating.
• Resolving Power of a grating is given as

19. Applications of Concepts
1. Diffraction gratings are capable of breaking white light into its
constituent colours. Prisms also carry out the same task.
Unlike in prisms, however, in a diffraction grating, deflection
of any specific colour is proportional to its wavelength. The
spectra produced by gratings are, therefore, easier to
calibrate compared to that produced by prisms.
2. Diffractive optics is also used in holography for
reconstructing three-dimensional images of objects using
laser light.