Waves Experiment 2
Thin Films
Safety
Make sure that you have read the safety notes in the introductory section of this manual before
beginning any practical work.
Do not, under any circumstances, attempt to repair any of the equipment should you think it to be
faulty. Rather, turn off the apparatus at the power-point and consult your demonstrator.
In the course of this experiment the lamps will become very hot. Be careful to ensure that you do
not burn yourself.
Preliminary Exercise:
In order to ensure that you fully understand how to analyse the results of this lab session, work
through the section under the heading "Sample Analysis" starting on the next page, which is very
similar to the analysis you will be required to perform during the lab. It will give you a chance to
apply the appropriate ideas for estimating uncertainties.
Outline:
In this laboratory exercise you will explore the interference fringes produced when two
approximately flat glass plates are in contact. You will then make a wedge shaped air gap by
inserting a hair between two glass blocks, at one end (see the diagram below). You should now see
closely spaced light and dark lines, the spacing of which is determined by the thickness of the hair
(unknown), the wavelength of the light (known) and the width of the block (which can be
measured). The spacing between the line can be measured and hence the diameter of the hair can
be calculated.
References
121/2:
Section 39.2.
141/2:
Section 36.7.
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Introduction:
The swirling colours of an oil film on
a puddle, bands of colour drifting
downwards in soap bubbles and
gloriously coloured butterfly wings
occur for basically the same reason
— light behaving like waves.
In this session you will come to understand why all of these thin films of material appear to be
coloured, and you will use this behaviour to measure the diameter of your own hair! The
interference effects caused by two rays of light give us a very powerful technique for measuring
small distances ("small" in this instance meaning of the order of several wavelengths of light).
Consider the diagram on the next page where an incident ray of monochromatic light is partially
reflected from two surface boundaries (glass-air and air-glass).
We will assume that the angle of incidence is very small (ie. ~ 0 degrees) and hence any
refraction effects will be small and can be ignored.
The intensity of the light beam reaching the eye (Ray 1 + Ray 2) is determined by the
Superposition Principle. That is, Rays 1 and 2 interfere and whether the intensity is at a
maximum or a minimum or at some intermediate value depends on the relative phase of Ray 1
and Ray 2.
The phase of Ray 2 is different to that of Ray 1 because Ray 2 travels a greater distance (this
greater distance is approximately 2t when  is small). As well, there are different phase changes
on reflection. Experiment shows that when Ray 1 is reflected at the glass-air boundary, it is
reflected without phase change. When Ray 2 is reflected at the air-glass boundary, its phase is
shifted by , equivalent to travelling an extra "distance" of /2 where  is the wavelength.
Looking down on the glass from above, we observe either no reflected light (dark areas), if the air
gap is of the correct thickness for destructive interference, or we observe reflected light (light
areas) if the gap is such that there is constructive interference. If the air gap thickness
changes across the surface, then we would expect to see areas of light and dark alternating.
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Physics 121/2 and 141/2 Laboratory Manual
Sample Analysis:
A student has carried out the measurements required to determine the thickness of a hair. She
placed the hair between two flat, circular glass plates and when looking at the plates from above
saw an interference pattern similar to the one shown in the diagram below (the spacing has been
greatly exaggerated):
The dark bands were due to destructive interference between the incident and the reflected light
rays (remember, the light ray reflected from the lower block experiences a 180 degree phase
change, whilst the other ray does not, so there will be a dark band where the plates are in
contact).
The small triangle representing the side view shows how the diameter of the hair can be
calculated from similar triangles:
 2
s

d
w
where
d = diameter of the hair
s = spacing of the dark bands
w = distance from hair to point of contact of glass blocks.
Hence, the diameter of the hair,
d
Question (a):
w
2s
Compare the pattern produced by a film with a thick hair at the edge and a
pattern with a thinner hair at the edge. Explain in words, and using the
equations above.
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There are uncertainties associated with measurements of both s and w, but we will assume that 
is so much more accurately known that we need not bother with its uncertainty (verify this, if you
wish).
The distance between bands was obtained by measuring the distance across many bands (about
20, or more). This was done using a travelling microscope, ie. a microscope that has a built-in
scale allowing her to move it and accurately measure the distance travelled. To obtain the
distance travelled, the student read the scale at the start and end of the travel, and then
subtracted the values. Suppose our student recorded the following results:
No. of band spacings
20 ± 0
- we assume accurate counting!
Distance from hair to edge of
( 4.00 ± 0.05) cm
- estimated error
( 589.3 ± 0.3 ) nm
- looked up in a reliable table
glass (w)
 of sodium light
Initial reading (cm)
Final reading (cm)
4.65
3.93
4.15
3.47
4.54
3.85
4.55
3.85
4.62
3.92
Distance (cm)
Mean distance
or
±
cm
±
%
Complete the table above, and use the half-range of the recorded data to estimate the error in the
mean distance.
Use the above data to calculate the spacing (s) between any two adjacent dark bands:
or
s
=
±
cm
s
=
±
%
Now you can calculate the diameter of the hair. As well, the associated error in the diameter of
the hair can be calculated by following the details given in Appendix A.
Show that the final value should be:
d = 0.0034 ± 0.0001 cm (or ± 4%)
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Note:
Be careful not to round off the numbers too much during the calculation.
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Experiment – general instructions
Handling and Care of Optical Surfaces:
The polished surfaces of optical glass must not be placed upon rough or dirty surfaces.
When two optical surfaces are to be brought into contact, make sure that both are clean.
Dust them with a soft clean camel hair brush, and place one upon the other gently. Only the
edges of the plates should be touched with the fingers.
Do not handle the glass, even by the edges, unnecessarily, as thermal expansion will show
up in the fringes. When it is necessary to handle optical materials, allow a few minutes for
the system to come to thermal equilibrium.
Do not attempt to make one surface slide over the other, as this will cause scratches if there
is dust present.
Illumination:
To obtain interference fringes in a thin film, an extended source of light is necessary. For single
wavelength fringes a sodium light will be used. The use of a diffusing screen is often helpful. The
alignment of all the components is critical for a good view of the interference fringes. Follow the
instructions provided on the bench or by your demonstrator.
To see the fringes clearly the eye should be focussed on the film of air between the blocks.
eye or
travelling
microscope
diffusing
screen
sodium
light
source
sodium
light
source
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glass reflector
optical
glass
blocks
Physics 121/2 and 141/2 Laboratory Manual
Section A:
Observation of Fringe Patterns
Optical Flats
Experiment A1:
Examine the fringe patterns observed when the two optically flat surfaces are in contact as shown
below. Note particularly whether or not the fringes are straight and equally spaced.
Note:
Some optical flats have one surface that is better than the other. This is indicated by
an arrow on the side of the optical flat. If there is no arrow on the side of the optical
flat then either side may be used.
Draw what you see and interpret your descriptions.
Question (b):
Is any departure from flatness of the two surfaces detectable?
Curved Surfaces
Experiment A2:
Examine the fringe patterns observed when the side of the glass slab labelled '–' is facing one of
the optical flats. The surfaces should be cleaned, using only the brush provided, until a minimum
number of fringes is observed.
+
–
Even at the points where the pieces appear to touch, it is likely that a thin layer of air will
cushion them. When the minimum pattern has been obtained, gently press down the centre of
the upper plate with the brush handle to expel the air cushion. Observe the movement of the
fringe pattern.
Repeat this procedure with the side of the glass slab labelled '+' facing one of the optical flats.
Question (c):
Explain how the movement of the fringe pattern is consistent with the
curvature of the glass surface as indicated by the '+' or '–' marks on it.
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Section B:
Measurement of the Diameter of a Hair (b.y.o.)
Vernier scales:
The travelling microscope has a vernier scale which you will need to read in order to calculate the
distance travelled. The vernier scale looks like this:
where the top and bottom of the vernier scale can slide relative to each other and the bottom scale
has 10 divisions squeezed into 9 divisions of the top scale. If the top of the vernier scale is moved,
then the vernier scale might look something like this:
By looking at the position of the "0" of the bottom scale (which was previously aligned with the "0"
of the top scale) we conclude that the two parts of the vernier have moved a relative distance of
1.3 and a bit units. The distance can be determined more accurately by counting along the bottom
scale and checking to see which of the bottom scale marks is aligned with a mark above it. In this
case the "8" mark on the bottom scale is aligned with a mark above it, hence the distance
travelled is 1.38 units.
When using the travelling microscope you will use the vernier scale to determine the starting
position and the ending position in the manner described above.
There will not be a travelling microscope on each desk, so you may have to wait until one is free to
use.
Experiment B
(i)
Place a hair between the two optically flat surfaces, at one end.
(ii)
Use the travelling microscope to measure the fringe spacing and hence obtain data from
which you can calculate the thickness of the hair.
(iii)
Measure the distance from the centre of the hair to the point of contact of the optically flat
surfaces.
(iv)
Record the data in a table similar to the one shown in the sample analysis.
(v)
Calculate the diameter of the hair (include error limits in your calculation).
Question (d):
What was the diameter of the hair?
Question (e):
What was the measurement that caused the largest uncertainty in your result?
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Question (f):
Why was a ruler able to give you a sufficiently precise measure of the distance
from hair to the edge of the wedge?
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