Physical optics -- counting interfence fringes to measure a length change

In summary, physical optics is a branch of physics that studies the behavior of light as a physical phenomenon, including reflection, refraction, diffraction, and interference. Interference fringes can be used to measure length changes by counting the number of fringes and using the known wavelength of the light source. This is possible because the number of fringes is directly proportional to the change in length, and the distance between fringes is equal to half the wavelength of the light. Instruments such as Michelson, Fabry-Perot, and Mach-Zehnder interferometers can be used to measure interference fringes. Practical applications of this technique include metrology, microscopy, and interferometric sensors, as well as precise measurements in the construction of instruments
  • #1
denniszhao
15
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Homework Statement
Monochromatic light with wavelength λ=650nm is used to determine the coefficient of thermal expansion, α, of a particular metal. The apparatus is shown below. Light is projected from above and passes through the glass and reflects off the cylinder with initial length l0=15.0cm. The gap between the glass and the cylinder is very thin. Consequently, the reflected light contains an interference pattern with alternating light and dark fringes. As the temperature of the cylinder is raised, it expands and the width of the gap decreases. A researcher observes 450 fringe shifts when the temperature increases by ∆T=40.0K. What is the coefficient of thermal expansion for the metal?
I was tryna combine this two formulas to find out the thermal expansion coefficient α but the answer is incorrect.
Relevant Equations
Thermal expansion: ∆l=l0*α*∆T
Optics: ∆l=mλ
B7447CF9-94F3-4E6F-8945-15E7042F2C70.jpg
 
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  • #2
I was tryna combine this two formulas to find out the thermal expansion coefficient α but the answer is incorrect.
Post your work, so we can try to find why and from where ...

Guidelines
 
  • #3
It looks like you did not consider that the light travels twice the distance between the back of the glass and the end of the rod.
 

FAQ: Physical optics -- counting interfence fringes to measure a length change

1. How does counting interference fringes measure a length change?

Counting interference fringes is based on the principle of interferometry, where the interference pattern created by the combination of two or more light waves can be used to measure small changes in length. When an object is placed in one of the beams of light, it causes a phase shift in the light waves, resulting in a change in the interference pattern. By counting the number of fringes that have shifted, the change in length can be calculated.

2. What is the accuracy of using interference fringes to measure length changes?

The accuracy of this method depends on the quality of the interferometer and the precision of the measurement of the fringe shifts. With modern interferometers, accuracies of less than a nanometer can be achieved.

3. Can this method be used for measuring any type of length change?

This method is most commonly used for measuring small length changes, such as changes in the order of micrometers or nanometers. It is not suitable for measuring large length changes, as the interference pattern becomes too complex to accurately count the fringes.

4. What are some common applications of counting interference fringes to measure length changes?

This method is commonly used in scientific research and industrial applications for precise measurements of length changes in objects, such as in materials testing, MEMS (Micro-Electro-Mechanical Systems) devices, and interferometric sensors. It is also used in fields such as astronomy and metrology.

5. Are there any limitations to using interference fringes for measuring length changes?

One limitation is that the object being measured must be transparent, as the method relies on the interference of light waves passing through the object. Additionally, environmental factors such as vibrations or temperature changes can affect the accuracy of the measurements.

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