ACKNOWLEDGMENT
Primarily I would thank God for being able to complete
this project with success.
Secondly I would like to express my special thanks of
gratitude to my principal as well as Physics teacher Mrs. Jane
Sherline Tonia who gave me the golden opportunity to do this
wonderful project on the topic Human health and disease,
which also helped me in doing a lot of research and I came to
know about so many things. I am really thankful to them.
Thirdly I would like to thank my parents and friends who
helped me a lot in finishing this project.
It helped me increase my knowledge and skills. Once
again thanks to all who supported me all through this process.
INDEX
1. Aim 1
2. Introduction 1
3. Diffraction 2
4. Diffraction patterns 2
5. Single slit diffraction 3
6. Single slit interference 5
7. Diffraction grating 8
8. Bibliography 11
AIM:
To study the phenomenon of diffraction of light.
INTRODUCTION:
The phenomenon of diffraction was first documented in
1665 by the Italian Francesco Maria Grimaldi. The use of
lasers has only become common in the last few decades. The
laser’s ability to produce a narrow beam of coherent
monochromatic radiation in the visible light range makes it
ideal for use diffraction experiments: the diffracted light
forms a clear pattern that is easily measured. As light or any
wave, passes a barrier, the waveform is distorted at the
boundary edge. If the wave passes through a gap, more
obvious distortion can be seen. As the gap width approaches
the wavelength if the wave, the distortion becomes even more
obvious. This process is known as diffraction. If the diffracted
light is projected onto a screen some distance away, then
interference between the light waves create a distinctive
pattern (the diffraction pattern) on the screen. The nature of
the diffraction pattern depends on the nature of the gap (or
mask) which diffracts the original light wave. Diffraction
patterns can be calculated by from a function representing the
mask. The symmetry of the pattern can reveal useful
information in the symmetry of the mask. For a periodic
object the pattern is equivalent to the reciprocal lattice of the
object. In conventional image formation, a lens focuses the
diffracted waves into an image. Since the individual section
(spots) of the diffraction pattern each contain information, by
forming an image from only particular parts of the diffraction
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pattern, the resulting image can be used to enhance particular
features. This is used in bright and dark field imaging.
DIFFRACTION
What is diffraction?
When parallel waves of light are obstructed by a very small
object (i.e,sharp end, edge slit, wire, etc.) the waves spread
around the edges of the obstruction and interfere, resulting in
a pattern of a dark and light fringes.
What does diffraction look like?
When light diffracts off of the edge of an object, it creates a
pattern of light referred to as a diffraction pattern. If a
monochromatic light source, such as laser, is used to observe
diffraction, below are some examples of diffraction patterns
that are a created by a certain objects.
DIFFRACTION PATTERNS
2
SINGLE SLIT DIFFRACTION
In our consideration of the Young’s double – slit
experiment, we have assumed the width of the slits to be so
small the each slit is a point source. Here we shall take the
width of slit to be finite and see how Fraunhofer diffraction
arises. Let a source of monochromatic light be incident on a
slit of finite width ‘a’, as shown in figure 1
FIGURE:- Diffraction of light by a slit of width ‘a’
In diffraction of Fraunhofer type, all rays passing
through the slit are approximately parallel. In addition, each
portion of the slit will act as a source of light waves according
to Huygens's principle. For simplicity we divide the slit into
two halves. At the first minimum, each ray from the upper
half will be exactly 180 out of phase with a corresponding ray
form the lower half. For example, suppose there are 100 point
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sources, with the first 50 in the lower half, and 51 to 100 in
the upper half. Source 1 and source 51 are separated by a
distance and are out of phase with a path difference a/2δ =
λ/2. Similar observation applies to source 2 and source 52, as
well as any pair that are a distance a/2 apart. Thus, the
condition for the first minimum is
Applying the same reasoning to the wave fronts from
four equally spaced points a distance a/4 apart, the path
difference would be δ = a sinθ/4, and the condition for
destructive interference is
The argument can be generalized to show that destructive
interference will occur when
Figure 2 illustrates the intensity distribution for a single-slit
diffraction. Note that θ = 0 is a maximum.
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Figure: Intensity distribution for a single-slit diffraction.
By comparing Eq. 14.5.2 with Eq. 14.5.4, we see that the
condition for minima of a single-slit diffraction becomes the
condition for maxima of a double-slit interference when the
width of a single slit a is replaced by the separation between
the two slits d. The reason is that in the double-slit case, the
slits are taken to be so small that each one is considered as a
single light source, and the interference of waves originating
within the same slit can be neglected. On the other hand, the
minimum condition for the single-slit diffraction is obtained
precisely by taking into consideration the interference of
waves that originate within the some slit.
SINGLE SLIT INTERFERENCE
How do we determine the intensity distribution for the
pattern produced by a single-slit diffraction? To calculate this,
we must find the total electric field by adding the field
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contributions from each point. Let's divide the single slit into
N small zones each of width Δy =a /N, as shown in Figure
14.6.1. The convex lens is used to bring parallel light rays to a
focal point P on the screen. We shall assume that Δy << λ so
that all the light from a given zone is in phase. Two adjacent
zones have a relative path length δ = Δy sinθ. The relative
phase shift Δβ is given by the ratio
Figure: Single-slit Fraunhofer diffraction
Suppose the wave front from the first point (counting from the
top) arrives at the point P on the screen with an electric field
given by
The electric field from point 2 adjacent to point 1 will have a
phase shift AB, and the field is
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Figure: Intensity of the single-slit Fraunhofer diffraction pattern
Figure: Intensity of single-slit diffraction as a function of θ for a = λ and a = 2λ
DIFFRACTION GRAFTING
7
A diffraction grafting consists of large number N of slits
each of width ‘a’ and separated from the next distance d, as
shown in figure
Figure: Diffraction grating
If we assume that the incident light is planar and diffraction
spreads the light from each slit over a wide angle so that the
light from all the slits will interfere with each other. The
relative path difference between each pair of adjacent slits is δ
= d sinθ, similar to the calculation we made for the double-slit
case. If this path difference is equal to an integral multiple of
wavelengths then all the slits will constructively interfere with
each other and a bright spot will appear on the screen at an
angle θ. Thus, the condition for the principal maxima is given
by
If the wavelength of the light and the location of the m-order
maximum are known, the distance d between slits may be
readily deduced. The location of the maxima does not depend
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on the number of slits, N. However, the maxima become
sharper and more intense as N is increased. The width of the
maxima can be shown to be inversely proportional to N. In the
following figure, we show the intensity distribution as a
function of β /2 for diffraction grating with N=10 and N=30.
Notice that the principal maxima become sharper and
narrower as N increases
Figure: Intensity distribution for a diffraction grating for (a) N =10 and
(b) N =30.
The observation can be explained as follows: suppose an
angle (recall thatβ= 2πa sinθ / λ) which initially gives a
principal maximum is increased slightly. If there were only
two slits, then the two waves will still be nearly in phase and
produce maxima which are broad. However, in grating with a
large number of slits, even though θ may only be slightly
deviated from the value that produces a maximum, it could be
exactly out of phase with light wave from another slit far
away. Since grating produces peaks that are much sharper
than the two- slit system, it gives a more precise measurement
of the wavelength.
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BIBLIOGRAPHY
https://en.wikipedia.org/wiki/Diffraction
http://staff.ustc.edu.cn/~bjye/em/MIT-ID.pdf
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https://leverageedu.com/blog/physics-project-for-class-
12/
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