This document certifies that a student completed a research project on the diffraction of light, detailing the historical context and principles of diffraction, particularly the use of lasers. It explains the relationship between wave interference and diffraction patterns, as well as the conditions for minima and maxima in single and double slit experiments. The document concludes with calculations related to fringe width for different light wavelengths.

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This is to certify that <NAME>, a student of class 12-B,
Roll number <X> has successfully completed the
research project on the topic “Phenomenon of
Diffraction of Light (Single Slit)”, under the guidance
of <NAME OF TEACHER>. The progress of the
report has been continuously reported and been in the
aforementioned teacher’s knowledge consistently.
References taken in making this project have been
declared at the end of the report.
PHYSICS TEACHER EXTERNAL EXAMINER

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The phenomenon of diffraction was first
documented in 1665 by the Italian Francesco

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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 in diffraction experiment:
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 of the wave, the
distortion become 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.

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The nature of the diffraction pattern depends on
the nature of the gap which diffracts the original
light wave. Diffraction pattern can be calculated by
a function representing the mask. The symmetry
of the pattern can reveal useful information on the
symmetry on the mask. For a periodic object.
In conventional image formation ,a lens focuses
the diffraction waves into an image. Since the
individual sections of the diffraction pattern, each
contain information, by forming an image from the
particular parts of the diffraction pattern , the
resulting image can be used to enhance particular
features. This is used in bright and dark field
imaging.

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WHAT IS DIFFRACTION?
When parallel waves of light are obstructed by a
very small object (i.e. sharp edges, slit, wire, etc.),
the waves spread around the edges of the
obstruction and interfere, resulting in a pattern of
dark and light fringes.
WHAT DOES DIFFRACTION LOOK LIKE?
When light diffracts off the edge of an object, it
creates a pattern of light, referred to as a
diffraction pattern. If a monochromatic light
source, such as a laser, is used to observe
diffraction. Here are some examples of diffraction
patterns that are created by certain objects.

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In our consideration of the Young’s double slit experiment,
we have assumed the width of the slits to be so small that
each slit is a point source. In this section 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 above.
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 the
Huygens’ Principle. For simplicity we divide the slit into two
halves. At the first minimum, each ray of the upper half will
be exactly 180 out of phase with a corresponding ray from
the lower half. Thus the condition for the first minimum is
a/2sinθ=λ/2 …. (1)
Sinθ=λ/a …. (2)
Applying the same reasoning to the wave fronts from four
equally spaced points a distance a/4 apart, the path
difference would be δ = sinθ/4, and the condition for
destructive interference is

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Sinθ=2λ/a ….. (3)
The argument generated to show that destructive
interference will occur when
asinθ=mλ m=…-3,-2,-1, 1, 2, 3…. (Destructive interference)
… (4)
Figure below illustrates the intensity distribution for a
single-slit diffraction. Note that θ=0 is a maximum.

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By comparing Eq. (3) and (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 is replaced by the separation between the two
slits.

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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 a single slit diffraction is obtained precisely by
taking into consideration the interference of waves that
originates within the same slit.

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FOR RED LIGHT- FOR GREEN LIGHT-
β = 4.3cm β = 3.6cm
D= 4m D= 4m
d=0.12mm d=0.12mm
β=2λD/d β=2λD/d
4.3= 2λ.4 / 0.00012 3.6= 2λ.4 / 0.00012
λ= 650nm (approx.) λ= 550nm (approx.)
where,
β= fringe width, D=distance between screen and
slit, d= distance between the slits.

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