Introduction
The effects of diffraction of
light were first carefully observed and characterized by Francesco
Maria Grimaldi. The results of Grimaldi's observations were published
in 1665.Diffraction
is the slight bending of light as it passes around the edge of an object. The
amount of bending depends on the relative size of the wavelength of light to
the size of the opening. If the opening is much larger than the light's
wavelength, the bending will be almost unnoticeable. However, if the two are
closer in size or equal, the amount of bending is considerable, and easily seen
with the naked eye.
In
the atmosphere, diffracted light is actually bent around atmospheric particles
 most commonly, the atmospheric particles are tiny water droplets found in
clouds. Diffracted light can produce fringes of light, dark or colored bands.
An optical effect that results from the diffraction of light is the silver
lining sometimes found around the edges of clouds or coronas surrounding
the sun or moon.
The phenomenon in which light waves
bend around corners of an object and their spreading into the geometrical
shadow of an object is called diffraction.
Classification
of diffraction phenomena
Diffraction phenomenon is broadly
divided into two groups, based on the method adopted to study diffraction
effects. They are 1) Fresnel class of diffraction 2) Fraunhofer class of diffraction.
S.No.

Fresnel
Diffraction

Fraunhofer
Diffraction

1

Source
and screen are at finite distance from the obstacle/aperture.

Both
the source and the screen are at infinite distance from the
obstacle/aperture.

2

Spherical/Cylindrical
wave front falls on the obstacle/aperture.

Plane
wave front falls on the obstacle/aperture.

3

No
lenses are used in Fresnel diffraction.

Converging
lenses are used to study Fraunhofer diffraction.

4

Waves
falling on the obstacle/aperture will not be in the same phase.

Waves
falling on the obstacle/aperture have the same phase.

5

Fresnel
diffraction is general case of diffraction, which reduces to Fraunhofer case
when the source and screen are at infinite distance from the
obstacle/aperture.

Fraunhofer
diffraction is a particular case of diffraction with source and screen at
infinity from the obstacle/aperture.

Diffraction
Grating
An arrangement consisting of a large number of equidistant
parallel narrow slits of equal width separated by equal opaque portions is
known as a diffraction grating.
The plane transmission grating is a plane sheet of
transparent material on which opaque rulings are made with a fine diamond
pointer. The modern commercial form of grating contains about 6000 lines per
centimetre.
The rulings act as
obstacles having a definite width ‘b’ and the transparent space between the
rulings act as slit of width ‘a’. The combined width of a ruling and a slit is
called grating element (e). Points on successive slits separated by a distance
equal to the grating element are called corresponding points.
Theory
MN
represents the section of a plane transmission grating. AB, CD, EF … are the
successive slits of equal width a and BC, DE … be the rulings of equal width b. Let e = a + b.
Let
a plane wave front of monochromatic light of wave length λ be incident normally
on the grating. According to Huygen’s principle, the points in the slit AB, CD
… etc act as a source of secondary wavelets which spread in all directions on
the other side of the grating.
Let
us consider the secondary diffracted wavelets, which makes an angle θ with the
normal to the grating.
The
path difference between the wavelets from one pair of corresponding points A
and C is CG = (a + b) sin θ. It will be seen that the path difference between
waves from any pair of corresponding points is also (a + b) sin θ
The
point P1 will be bright, when
(a
+ b) sin θ = m λ where m = 0, 1, 2, 3............
In
the undiffracted position θ = 0 and hence sin θ = 0.
(a
+ b) sin θ = 0, satisfies the condition for brightness for m = 0. Hence the
wavelets proceeding in the direction of the incident rays will produce maximum
intensity at the centre O of the screen. This is called zero order maximum or
central maximum.
If
(a + b) sin θ1 = λ, the diffracted wavelets inclined
at an angle θ1 to the incident direction, reinforce and the first order maximum
is obtained.
Similarly,
for second order maximum, (a + b) sin θ2 = 2λ
On
either side of central maxima different orders of secondary maxima are formed
at the point P1, P2.
In
general, (a + b) sin θ = m λ is the condition for maximum intensity, where m is
an integer, the order of the maximum intensity.
sin
θ = Nmλ
where
N = 1/(a+ b) , gives the number of grating element or number of lines per unit
width of the grating.
When white light is used, the
diffraction pattern consists of a white central maximum and on both sides
continuous coloured images are formed.
In the undiffracted position, θ = 0 and
hence sin θ = 0. Therefore sin θ = Nmλ is satisfied for m= 0 for all values of
λ. Hence, at O all the wavelengths reinforce each other producing maximum
intensity for all wave lengths. Hence an undispersed white image is obtained.
As
θ increases, (a + b) sin θ first passes through λ/2 values for all colours from
violet to red and hence darkness results. As θ further increases, (a + b) sin θ
passes through λ values of all colours resulting in the formation of bright
images producing a spectrum from violet to red. These spectra are formed on either
side of white, the central maximum.
Determination
of wavelength of light (Normal Incidence)
The wavelength of white light can be determined using a plane diffraction grating and a spectrometer. The preliminary adjustments of the spectrometer are made. The slit of the collimator is illuminated by a mercury vapour lamp and the slit and the collimator are suitably adjusted to receive a narrow, vertical image of the slit. The telescope is turned to receive the direct ray, so that the vertical slit coincides with the vertical cross wire. The telescope reading is taken.
The grating is mounted on the prism
table. The telescope is now moved exactly through 90° and fixed in that
position. The prism table is rotated until the reflected image coincides with
the point of intersection of the crosswires. Now the angle of incidence is 45°.
The prism table is fixed in this position. The vernier disc is released and
rotated through 45° so that the light from the collimator is normally incident
on the grating.
The telescope is now released and
turned to receive the direct image. It is gradually moved to the left so that
the first order diffracted image (Violet to Red) is seen. After making the
point of intersection of the cross a wire to coincide with the image, the
telescope reading is taken. The telescope is then moved to the right and the
reading corresponding to the first order image is taken as before. Half the
difference between the two readings gives the angle of diffraction θ.
sin
θ = Nmλ
For the first order m=1. The number of
rulings per unit length N is provided by the manufacturer. It can also be
determined using light of known wavelength. Hence the wavelength λ can be
calculated.
The readings are tabulated as shown
below:
Order

Colour

Vernier
Reading

2θ

θ

λ


Left

Right


I


II

Zone
Plate
A
zone plate is a transparent plate divided into half period zones and designed
so as to cut off light through even numbered or odd numbered zones.
A
zone plate is an optical device, which works on the principle of Fresnel’s
zone. In Fresnel’s zones, the effect at a point due to alternate zones cancels
each other. If the effect of either even or odd zones is blocked at that point,
then the net effect due to alternate zoneshaving a path difference of λhas a
maximum value. A plate, which allows only one set of alternate zones of the
wavefront to pass through it, is called a zone plate.
The
radius of the zones is proportional to square root of n, where n = 1, 2, 3, etc. This property
isused in the construction of a zone plate. On a drawing sheet, concentric
circles are drawn with the radii proportional to square root of natural numbers
as shown in the following figure.
The alternate
zones are painted black. A photograph of the pattern is taken. We get on
developed negative a reduced pattern. This negative forms the zone plate. In
this plate alternate zones are transparent and allow light and the remaining
alternate zones act as opaque region. There are two types of zone plates. i) Positive
zone plate and ii) Negative zone plate as shown in figure (1a) and (1b).
(1) Positive zone
plate: A zone plate in which odd zones are transparent and even zones are opaque
is known as a positive zone plate.
(2) Negative zone
plate: A zone plate in which even zones are transparent and odd zones are opaque
is known as a negative zone plate.
References:
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/opt/mch/diff.rxml
http://www.readorrefer.in/article/DiffractiongratingexplanationwithTheory_568/
Optics – R.K.Agrawal, Garima Jain, Rekha Sharma, Krishna
Prakashan Media(P) Ltd, Meerut, First edition 2006.
http://veerashaivacollege.org/images/stories/Diffraction_New2.pdf