Thermal expansion coefficient of BK7 glass.
The thermal expansion coefficient will be measured in the material BK7 Glass. We use an
interferometric method whereby light is reflected from both the front and back surface of a lens.
A laser is sent through a small aperture toward the lens. The aperture is on a screen that can be
used to observe the back reflection in a dark room. After shining a laser upon the lens, the user
will notice reflective spots from each of the two surfaces. A perfect alignment of the lens
(translational and tilt) will cause the two spots to overlap and also to be centered on the incoming
laser path. Considerable effort should be taken to ensure the alignment is perfect. Good
alignment results in a brighter pattern.
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The lens is mounted in a standard lens holder with several thermocouples connected. The entire
mount is placed in a simple water heater flue pipe with an observation hole cut into it. There are
no windows or other optics that could cause their own pattern or obscure the interference pattern
we are looking at. A heat gun is placed at one end of the flue pipe and heat rises through the
pipe, enveloping the lens in a uniform temperature region (this has been checked with several
thermometers and thermocouples). Hot air flows out the optical port.
As the lens is heated, interference fringes are observed to move. The motion of the fringes is a
direct indication of the change in thickness of the lens.
Linear thermal expansion is defined as:
𝛼=
∆𝐿
𝐿𝑜 ∆𝑇
Where L is the change in width of the lens, Lo is the width of the lens at the initial temperature,
and T is the change in temperature.
Prior to heating the lens is initially at room temperature. The lens is heated to a maximum
temperature of about 65Co which ensures that no internal mounting pieces melt. The lens is
heated until it reaches equilibrium. At equilibrium you will observe the temperature does not
change, but also the fringe pattern stops moving.
The relation between the change in width of the lens and fringe count is:
2∆𝐿 = (∆𝑚)
𝜆
𝑛
Where m is the number of fringes that pass by as the temperature changes, is the wavelength
of the Helium Neon laser used, and n is the index of refraction of the lens AT this wavelength.
Tasks: Determine the thermal coefficient of expansion, , for BK7 glass and compare to the
known (there are a couple of values cited for different temperature ranges---our appropriate
number is 8.3x10-6/Co you may see the number 7.1….out there, it is measured for a differently
centered temperature range).
Above and beyond. Get good video. Come up with a good analysis technique (peak finding on
matlab), or other. Be able to measure fringe count to a hundredth of a fringe (I’ll be impressed).
You may not take the lens out of this oven (difficult), but you may measure the coefficient for
another lens (unknown material) if you construct your own oven. You may also discuss and
compare to other types of thermal expansion measurements (the purpose of ours is its simplicity
and robustness). Modify experiment for –not a lens---? Flat plate geometry, Newton’s rings
geometry, Wedge geometry??????????? Improve the temperature measurement and issues.
Come up with a way to broaden temperature range. Come up with a way to measure thermal
expansion as a function of T (high precision needed).
Other critical information:
The measured width of the lens using a micrometer is L=0.01003m ±0.00002m using a
micrometer. The tabulated index of refraction for the HeNe wavelength is n=1.51509.