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Thin Film Interference: Tips & Tricks

Thin Film Interference: Tips & Tricks

Problem Solving Guide

Algorithm

 (1) Sketch out the standard representation for thin-film interference: two horizontal lines, representing 3 separate media. Label on this sketch the indices of refraction of the three media. The middle medium is the "thin film."

(2) Determine the wavelength $\lambda_2$ of your wave inside of the thin film. Remember that maximum constructive interference has to do with whether or not some integer-number of wavelengths fit into some distance, so it is important to know what the wavelength is inside of the medium in which the path-length-difference occurs - which, if you use the standard sketch, is always the middle (or second) medium.

(3a) Determine which equation is appropriate for describing constructive interference. To do this, determine whether or not there is a relative phase-shift between the two waves that are interfering. Remember that, at every boundary, some light is transmitted while some is reflected. The reflected light will have a $\pi$ phase-shift if the index of refraction of the medium the wave is traveling into is greater than that which it is leaving. Using the standard sketch, this means the wave reflected off the top surface will have a phase-shift iff $n_2 > n_1$ and the wave reflected off the second surface will have a phase-shift iff $n_3 >n_2$. Transmitted light does not undergo a phase-shift.

(3b) If there is a $\pi$ relative phase shift, then: 

  • constructive interference is described by $2t = \left(m + \frac{1}{2}\right) \lambda $, where $t$ is the thickness of the thin film and $\lambda$ is the wavelength of the light within the thin film (so here it takes the value of $\lambda_2$ calculated above, but I have left it as $\lambda$ to be consistent with other resources). 
  • destructive interference is described by $2t = m \lambda$

If there is no relative phase shift between the two waves, then the equations are swapped and $2t = m \lambda$ corresponds to constructive and $2t = \left( m + \frac{1}{2} \right) \lambda$ corresponds to destructive interference.

You now have all of the variables you need to finish the problem. Depending on the problem, you may be asked for a couple of different things. One might be a "minimum thickness" - in this case, you want to find the minimum possible value you can find for $t$, which corresponds to the smallest possible $m$ value (usually either $0$ or $1$). Or, you may be asked what wavelengths would produce destructive or constructive interference given some thickness - which is as simple as solving $2t = m \lambda$ for $t$ (or the other equation, depending on the situation). Once you have gone through step 3 above, you have all of the info that can be gleaned algorithmically: the rest is down to correctly interpreting the individual problem and what it is asking for. 

Misconceptions & Mistakes

  • There is not one simple equation for thin-film interference - the conditions for maximum and minimum interference change based on the parameters of the problem. You must first determine if there are relative phase shifts!

Pro Tips

  •  Always draw the same picture for thin-film interference problem: two horizontal lines, labelling the indices of refraction of the different media. This will help you get your bearings on the problem and get most of the relevant information on the page
  • Being good at thin-film intererence problems is all about identifying phase-shifts, since understanding the relative phase-shift between two waves is what dictates which equations to use. Always find phase-shifts first, if you are able, before continuing on the problem.

Multiple Representations

Multiple Representations is the concept that a physical phenomena can be expressed in different ways. 

Physical

Physical Representations describes the physical phenomena of the situation in a visual way.

 

Mathematical

Mathematical Representation uses equation(s) to describe and analyze the situation.

A representation with the words thin film interference on the top with a note constructive without relative phase shift between first reflected ray and the second reflected ray. There is an equation that shows that the twice the thickness of the film is equal to the product of the m-value and the wavelength of light in the film. This is also written in words below.

A representation with the words thin film interference on the top with a note constructive with relative phase shift between first reflected ray and the second reflected ray. There is an equation that shows that the twice the thickness of the film is equal to the m-value plus one half multiplied by the wavelength of the light in the film. This is also written in words below.

A representation with the words thin film interference on the top with a note destructive without relative phase shift between first reflected ray and the second reflected ray. There is an equation that shows that twice the thickness of the film is equal to the m-value plus one half multiplied by the wavelength of the light in the film. This is also written in words below.

A representation with the words thin film interference on the top with a note destructive with relative phase shift between first reflected ray and the second reflected ray. There is an equation that shows that twice the thickness of the film is equal to the product of the m-value and the wavelength of light in the film. This is also written in words below.

Graphical

Graphical Representation describes the situation through use of plots and graphs.

 

Descriptive

Descriptive Representation describes the physical phenomena with words and annotations.

 

Experimental

Experimental Representation examines a physical phenomena through observations and data measurement.

 

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