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#24 Interference of Light Waves
Objective
The objective of this experiment is to observe various manifestations of the interfer
ence of light waves.
Introduction and Theory
Because light has a wave nature it can exhibit the same phenomena that, say, water
waves do when they interact with sharp boundaries or with other waves. The effects of
interaction include reflection, refraction, diffraction, and interference. The effects of dif
fraction and interference will be the subject of this laboratory.
I. The Diffraction Grating
The diffraction grating consists of a very large number of fine, equally spaced paral
lel slits. There are two types of diffraction gratings: the reflecting type and the transmit
ting type. The lines of the reflection grating are ruled on a polished metal surface: the
incident light is reflected from the unruled portions. The lines of the transmission grating
are rule on glass: the unruled portions of the glass act as slits. Gratings have typically be
tween 100 to 800 lines per millimeter. A diffraction grating provides the simplest and
most accurate method for measuring wavelengths of light.
The principles of diffraction and interference are applied to the measurement of
wavelengths with a diffraction grating. Let the vertical broken line in Fig. 24.1 represent a
magnified portion of a diffraction grating. Let a beam of parallel monochromatic light,
originally from a single source and having passed through a slit, impinge upon the grating
from the left. By Huygens' principle, the light spreads out in every direction from the ap
ertures of the grating, each of which acts as a separate new source of light. The envelope
of the secondary wavelets determines the position of the advancing wave. In Fig. 24.1 we
see the instantaneous positions of several successive wavelets after they have advanced
beyond the grating. Lines drawn tangent to these wavelets connect points which are in
phase: hence they represent the new wave fronts. One of these wave fronts is tangent to
wavelets which have all advanced the same distance from the slits, and the wave front
formed is thus parallel to the original wave front. A converging lens placed in the path of
these rays would form the central image. Another wave front is tangent to wavelets whose
distances from adjacent slits differ by one wavelength. This wave front advances in the
direction 1 and forms the firstorder image. The next wave front is tangent to wavelets
whose distances from adjacent slits differ by two wavelengths. This wave front advances
in the direction 2 and forms the secondorder image. Images of higher orders will be
found at correspondingly greater angles.
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Max
Max
Max
Incident
Max
Wave
S2
Max
Max
Max
THEN
So
Max
Max
Max
Si
Max
Max
Max
с
B
Fig. 24.1. Interference patterns resulting from waves incident on two slits
of a grating
Let be the wavelength of the light, m the order of the image (m= 1 for the first
order image, m = 2 for the secondorder image, etc.) formed on either side of the central
(m= 0) image, d the distance between slits (a diffraction grating consists of several equal
lyspaced slits), and the angle of deviation from the original direction of the light. These
four quantities are interrelated by the grating equation,
m2 = d sin e
(24.1)
The angle O is measured directly, while the grating constant d is calculated from the
number of lines per millimeter ruled on the grating. If the light is monochromatic, a single
image of the slit will appear in each order.
 Grating
12
11
Source
ө
Y
Slit
11
Observer
12
Fig. 24.2 Viewing diffractionproduced (virtual) images of a slit through a grating.
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If the light is polychromatic, however, there will be as many images of the slit in each
order as there are different wavelengths in the light from the source, the diffracting angle
for each wavelength being given by the above equation. The resulting pattern of multiple
lines in the first order is known as the firstorder spectrum, that in the second order is the
secondorder spectrum, and so on. Spectra produced in this manner will be discussed in
detail in Experiment #24.
ni
12
13
11
t
Fig. 24.3. Interference of two beams incident on the left and right boundaries of a thin film.
II. ThinFilm Interference
Interference is the combining by superposition of two or more waves that meet at
one point in space. Thinfilm interference can be understood as the combining by super
position of rays reflected from opposite sides of the thin film. Examples of thin films are
soap films, lens coatings, or a thin wedge of air formed between two glass plates as shown
in Fig. 24.3.
Ray rı is reflected from the left surface of the film and ray r2 is reflected from the
right surface. If t is the thickness of the air wedge at the point where ray rı strikes it, then
ray r2 will travel a distance 2t further than ray rı. Therefore, if the rays were in phase be
fore they reached the wedge, when they combine they will no longer be in phase.
Three effects must be taken into account in determining the net result of this type of
superposition. First, not only does a ray undergo a partial reflection when encountering
another medium (glasstoair or airtoglass), but it may also experience a 180° phase shift
(which corresponds to a shift of 1/2 in the wavetrain). A 180° phase shift occurs whenever
the index of refraction of the first medium is less than that of the second (e.g., airto
glass). Such a change of phase does not occur, however, when the index of refraction of
the first medium is greater than that of the second (e.g., glasstoair). Because of this ef
fect, the two rays will travel essentially the same distance (assuming t«< 2 in Fig. 24.3),
but ray T2 will experience a 180° phase shift upon reflection while ray rı will experience
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no phase shift at all. Therefore, the two rays will emerge from the film 180° out of phase
and subsequently combine destructively. This region of the film will appear dark to an
observer's eye.
The second effect involves the fact that a depends on the index of refraction, n. If a
is the wavelength in a vacuum, the corresponding wavelength in a medium of index of
refraction n, an, is given by
a
an
(24.2)
n
This is important because the extra distance traveled by one of the two rays is al
ways traveled in the thin film, so it is in that should be used to determine whether or not
there is constructive (bright) or destructive (dark) interference. For the situation depicted
in Fig. 24.3, 2n = 2 because the index of refraction of air is 1.00.
The third effect is a path difference which arises between the two rays when the film
thickness is nonnegligible. In the discussion of the phase shift given above, we assumed
for simplicity that t«< 1, so that the two rays would always emerge from the film 180°
out of phase. If, however, the distance traveled by ray r2 in the film is an appreciable frac
tion of the wavelength, then this ray will be effectively shifted back (relative to ray rı) by
an amount equal to twice the thickness of the air film. For example, if 2t = 122, then ray r2
will be shifted back by exactly half of one wavelength; this effectively cancels the 180°
phase shift, thus yielding constructive interference (bright). Similarly, constructive inter
21
ference would result for 2t = ža, z ł, ż 1, etc. If, on the other hand, 2t = 1, then ray 12
will be shifted back by exactly one wavelength, so that the 180° phase shift yields destruc
tive interference (just as in the case where t was negligible compared with 2). Similarly,
destructive interference will occur when
2t = 27, 37, 41, 52, etc. In general, the, the condition for destructive interference at ap
proximately normal incidence of light is
3
5
2t = min
(m= 0, 1, 2, 3, ...)
(24.3)
where 2t (twice the film thickness) is the path difference between the two rays, m is a pos
itive integer, and in is the wavelength of light in the film.
When a wedge of film is used the film thickness varies from essentially zero near the
apex of the wedge to a maximum thickness t. To illustrate the effects described above,
suppose that light of wavelength 1 = 2n = 500 nm illuminates at approximately normal
incidence a film of thickness
t = 0.01 nm = 10 um = 10,000 nm. Then the extra distance traveled by ray r2 (i.e., the
path difference between the rays) is 2t = 20,000 nm = 20,000 nm/500 nm = 40 wave
lengths, so there will be 40 changes (interference fringes) from dark (destructive) at the
apex of the wedge to bright (constructive) where the thickness is t. More importantly, if
the number of interference fringes can be counted between two points on the film, then the
difference in thickness between those two points can be calculated, and so this technique
can be used to measure very tiny dimensions such as the diameter of a human hair.
Apparatus

The following equipment will be needed:
monochromatic light source (1 = 546.1 nm)
mercury vapor discharge tube with highvoltage power supply
optical bench
ruled Tbar with slit
100, 300, and 600 line/mm diffraction gratings
optical flat
glass microscope slide


Experimental Procedure
I. Diffraction Grating
The arrangement used in this experiment is shown in Fig. 24.2. Light from a mono
chromatic source passes through a narrow slit and falls on the grating. The observer looks
through the grating in the direction of the light source and sees the central (zerothorder)
image and the diffracted beams which make up the successively higherorder images
(first, second, etc.) on either side of the central image. The measuring scale should be
mounted horizontally and perpendicular to the central ray. The grating should be mounted
parallel to the scale about 50 cm away from it and with the grating rulings parallel to the
slit.
1. Mount the 100 lines/mm grating and slit with the scale on the optical bench, with the
grating rulings parallel to the slit and the plane of the grating and the slit with the scale
both perpendicular to the central ray.
2. Place the monochromatic light source in position behind the slit. Look through the dif
fraction grating in the direction of the source. Keep your eye several inches away from
the grating. As discussed above you will see the source and virtual images of the source
on either side. Carefully move the grating holder forward toward the slit until the first,
second, and thirdorder slit images are positioned clearly on the scale on each side of
the central (zerothorder) image. A slight adjustment can perhaps be made to render
both the lefthand and righthand image distances equal. Measure and record the dis
tance between the slit and the grating. do not change the position of the grating until the
next grating is used.
3. Look through the grating at the first, second, and thirdorder (virtual) images on the
righthand side. Record the apparent position and each image on the Tbar scale. Re
peat for the lefthand side.
4. Repeat steps 13 for the 300 lines/mm grating.
5. Repeat steps 13 for the 600 lines/mm grating. (Note: You will only be able to observe
the first two orders.)
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