2. PRESENTATION ON
INTERFERENCE
SUBMITTED-BY SUBMITTED TO-MRS RAMNA TRIPATHI
PARAS SUNDRIYAL
BRANCH -CSE

3. ACKNOWLEDGMENT
I Paras Sundriyal of CSE -1 ST branch 2022-2023 feels very
great to present you the slides on the topic Interference. I
show my gratitude to the Dean Academics, Dr Ramna
Tripathi for giving me the golden chance to explore on the
concept of interference beyond our syllabus. This not only
helped us to gain good score but also making our concepts
clearer. Hope you like the presentation and gain relevant
content.

4. CONTENTS
• Definition
• Coherent Sources
• Conditions for interference
• Constructive and Destructive interference
• Classification of interference
• Young double slit’s experiment(YDSE)
• Fringe width
• Displacement of fringes
• Stoke’s treatment
• Newton’s rings
• Thin film and wedge shaped film

5. INTERFERENCE
• Interference of light is the phenomena of multiple light waves interacting
with one another under certain circumstances, causing the combined
amplitudes of the waves to either increase or decrease.
• Most people observe some type of optical interference every day, but do
not realize what is occurring to produce this phenomenon. One of the
best examples of the interference of light is demonstrated by the light
reflected from a film of oil floating on water.

6. COHERENT SOURCES
• Two light waves are said to be coherent if they emit
continuous light waves of same frequency or wavelength ,
same or constant phase difference.
• Two independent sources of light can never be coherent
because it is practically impossible that they may emit light
waves of same phase or constant phase difference.
• Hence two coherent sources are made by different methods
latter discussed in the presentation

7. CONDITION FOR INTERFERENCE
• Two sources of light must be coherent.
• Sources must be narrow . A broad source is equivalent to a number of
narrow sources placed side by side . Each pair will produce its own
interference pattern and different patterns will overlap.
• Distance between sources and screen should be large . This increase the
fringe width and hence fringes become more prominent .
• Distance between sources should be small . This also increases fringe
width .
• Amplitude of light waves from two sources should preferably
monochromatic if sources are white we get a central white fringe
surrounded by a few coloured fringe and their general elimination occurs
due to overlapping of different colours.

8. Constructive interference
• If the crest of one wave falls on the
crest of another wave, then the
amplitude of the wave became
maximum and it forms the constructive
interference of light. Here, the
resultant waves will have the same
phase and the same displacement.
Destructive interference
• If the crest of one wave falls on the
dip of another wave, then the
amplitude of the wave becomes
minimum. This phenomenon is called
destructive interference. Here, the
phase and displacement of the
resultant wave are not the same.

9. CLASIFICATION OF INTERFERENCE
• The production of two interfering beams of light from a same source can be
studied under 2 main headings.
• Division of wavefront: In this case wavefront is divided into parts by utilizing the
phenomenon of reflection , refraction or diffraction in such a manner that the two
parts must form coherent sources.(YDSE).
• Division of amplitude: In this case we get two or more beams from a single wave
by partial reflection or refraction . These waves are then made to interfere
because they satisfy the requirements of coherence.(NEWTON’S RING).

10. YOUNG’S DOUBLE SLIT
EXPERIMENT(YDSE)
• In 1801 Thomas Young provided the first experimental evidence for the wave theory of light
from double slit interference experiment. Young allowed the sunlight to pass a through a pin
hole So on first screen followed by S1 and S2 at some distance on second screen as shown in
figure. On the screen he observed few colored bright and dark bands. To increase the
brightness of bands the pin holes S1 and S2 are replaced by narrow slits and to increase the
number of fringes sunlight is replaced by monochromatic source. Finally the interference
pattern consists of equally spaced bright and dark fringes are obtained.
• Spherical wave came out as the sunlight passes through the pin hole So, (as per Huygen’s
wave theory), the radii of these waves increases as they move away from So, when these
spherical waves reaches the second screen again spherical waves came out from S1 and S2,
these waves move away from S1 and S2 and hence they superimpose on each other. At the
point where wave crest (or trough) of one wave fall on the wave crest (trough) of other, the
resultant amplitude is maximum (maximum intensity, as I = A2) and where the wave crest of
one fall on the wave trough of other, the resultant intensity is minimum. In this way large
number of dark and bright bands are formed on screen.

12. FRINGE WIDTH
• Fringe width is that the distance between two successive bright fringes or two successive dark
fringes. within the interference pattern, the fringe width is constant for all the fringes. Fringe width is
independent of order of fringe. Fringe width is directly proportional to wavelength of the light used
it's given by
β=λDd
Where “D” is the distance of slit to screen and “d” is the distance between the slits.
λ is the wavelength of light used.

13. DISPLACEMENT OF FRINGES
• Displacement of fringes is the apparent movement of interference fringes when
observed from a different position. This displacement is due to the difference in
path length between the two waves. When viewed from the side, the
displacement is equal to the difference in path length divided by the wavelength.
• Displacement is caused by the difference in path length between two waves.
When two waves meet, they will interfere with each other. If one wave has
traveled a longer distance than the other, it will have a different phase when they
meet. This difference in phase will cause the displacement of fringes.

14. THIN FILM
When a film of thickness ’t’ and refractive index 'm' is introduced in the
path of one of the sources, then fringe shift occurs as the optical path
difference changes.
Optical path difference at
P = S2P - [S1P+ µt - t] = S2P - S1P - (µ - 1)t = y.d/D - (µ - 1)
⇒ nth fringe is shifted by Δy = D(µ-1)t/d = w/λ (µ-1)t

15. STOKES TREATMENT
• According to refraction : When the light ray moves air to denser
then the ray bent toward the normal. When the light ray moves
denser to air then the ray bent away from the normal. So, When the
light ray moves air to denser then the ray will be reflect and the
phase change will be π.
• Hence, The change of phase when reflection takes place at a
denser medium is π.This is stokes treatment.

16. NEWTON’S RINGS
• When a plano-convex lens with its convex surface is placed on a plane glass
plate, an air film of gradually increasing thickness is formed between the lens and
the glass plate. The thickness of the air film is almost zero at the point of contact
O and gradually increases as one proceeds towards the periphery of the lens. If
monochromatic light is allowed to fall normally on the lens, and the film is
viewed in reflected light, alternate bright and dark concentric rings are seen
around the point of contact. These rings were first discovered by Sir Isaac
Newton, hence named as Newton's Rings. If it is viewed with the white light then
coloured fringes are obtained. The experimental arrangement of the Newton’s
Ring apparatus is shown in figure 1.

17. A parallel beam of monochromatic light is reflected
towards the lens L. Consider a beam of monochromatic
light strikes normally on the upper surface of the air film.
The beam gets partly reflected and partly refracted. The
refracted beam in the air film is also reflected partly at the
lower surface of the film. The two reflected rays, i.e.
produced at the upper and lower surface of the film, are
coherent and interfere constructively or destructively.
When the light reflected upwards is observed through
microscope M which is focused on the glass plate, a
pattern of dark and bright concentric rings are observed
from the point of contact O. These concentric rings are
known as Newton's Rings.
The path difference between the two successive reflected
rays are obtained using wedge shaped interference case
as: = 2t cos(r + )+- / 2 (1) For air film, = 1 and at
normal incidence, i = r = 0. Since, is very small then cos
=1. Hence, eq. (1) reduces to = 2t +- / 2 . At the point of
contact of the lens and the glass plate (O), the thickness of
the film is effectively zero i.e. t = 0
= / 2 . This is the condition for minimum intensity.
Hence, the center of Newton rings generally appears dark.