Polarization Reflection question

[BobbyBobbyBob]

A thin film of ethyl alcohol (n=1.36) is spread on a flat glass plate and illuminated with white light. When illuminated and viewed from directly above, it shows a coloured pattern in reflection. If the only visible light reflected by a certain region of the film is yellow (lambda=560nm), how thick is the film there? Justify (assume visible spectrum is 400-7800nm)



I have no idea where/how to start and what it involves.

I have a feeling it invovles Huygen's Principle and Polarization by Reflection.

 

[berkeman]

What thicknesses of ethyl alcohol will result in the yellow light reflected off the top surface and the yellow light reflecting off the alcohol-glass surface being in phase as they head back up to the observer?

 

[kyle8921]

I can provide an explanation for this phenomenon using the principles of optics and the properties of thin films. Firstly, when white light is incident on the thin film of ethyl alcohol, it undergoes multiple reflections and interference within the film. This results in certain wavelengths of light being enhanced or suppressed, leading to the observed colored pattern in reflection.

Now, let's focus on the region where only yellow light (560nm) is reflected. This means that the thickness of the film at that particular region is such that only the yellow wavelength experiences constructive interference, while other wavelengths experience destructive interference. This is known as the "constructive interference condition".

According to Huygen's principle, every point on a wavefront can be considered as a source of secondary wavelets. In the case of reflection from a thin film, the reflected wave from the top surface interferes with the wave reflected from the bottom surface. The path difference between these two waves determines whether constructive or destructive interference occurs.

In this case, the path difference between the two reflected waves must be exactly one wavelength of yellow light (560nm) for constructive interference to occur. This can be represented mathematically as:

2nt = mλ

Where:
n is the refractive index of the film (1.36)
t is the thickness of the film at that particular region (unknown)
m is an integer representing the order of interference (in this case, m=1 for constructive interference)
λ is the wavelength of light (560nm)

Rearranging this equation, we can find the thickness of the film at that region:

t = (mλ)/(2n)

Substituting the values, we get:

t = (1 x 560nm)/(2 x 1.36) = 206.9nm

Therefore, the thickness of the film at the region where only yellow light is reflected is approximately 206.9nm. This is within the visible spectrum of light (400-780nm), which justifies our assumption.

In conclusion, the colored pattern observed in reflection from the thin film of ethyl alcohol can be explained by the principles of interference and polarization. By considering the constructive interference condition and using the formula for path difference, we were able to determine the thickness of the film at a region where only yellow light is reflected.