A Mach-Zehnder interferometer can also be used to measure the thickness of a tra

Question

A Mach-Zehnder interferometer can also be used to measure the thickness of a transparent material. But it is only easy for very small thicknesses, because even 1 mm of glass would be equivalent to thousands of wavelengths. However it is ideal for measuring tiny changes of length of transparent crystals. Consider a glass slide, 5.0 mm thick. Its coefficient of thermal expansion may be taken to be 9 Times 10^-6 degree C^-1 and its refractive index to be 1.5 and constant (we choose to ignore any changes in refractive index resulting from temperature variations). If this slide were in one arm of a Mach-Zehnder interferometer with a HeNe laser as the source (lambda = 632.8 nm) and if the temperature in the laboratory were to increase by 10 degree C, by how much would the output intensity at the detector change? Conceptual problem: A thin film of soapy water on a wire loop is inserted into the test volume of a Mach-Zehnder interferometer so that the film is perpendicular l to the HeNe laser probe beam. The detector is replaced camera lens, and the output beam is recorded as this graph.

Explanation / Answer

I = lambda/2(n-1)

t = lambda/4n

if temprature increase then

dt = t*alpha*dt

dt = 5*9x10^-6 * 10

t' = 5.00045 x 10^-3 m

t' = 5.00045 mm

n = real thickness / appearent thickness

I = 632.8 x 10^-9 / 2 ( 1.5 -1)

I = 6.328 x 10^-7

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