Interference in Thin Films: Grade 12 Optics Review

[EmilyBergendahl]

Homework Statement

Would you see the same thin film interference pattern in a film of soap surrounded by air and a film of soap on glass? Why or why not?

Homework Equations

None

The Attempt at a Solution

Yes, you would see the same thin film interference pattern in a film of soap surrounded by air and a film of soap on glass. In thin films of soap and oil, visible colour bands are the result of interference of light. In this situation, the interference is caused by the interference of light waves reflected from the opposite surfaces of thin films, therefore, the phase change is negligible to the pattern produced.

Here are two images from my textbook (Nelson Physics 12) that show the scenario. They appear to be almost the same, except for the phase change to glass in the first image. Does the phase change affect the interference pattern that the viewers see? Or are rays 1-3 the only ones of importance in the pattern?

Any clarification is much appreciated!

 

[Charles Link]

The "no phase change" arrow on the lower right on the diagram on the right is really pointing to the wrong place. The "no phase change" arrow should point to the point of reflection of ray 1 going to ray3 off of the "lower" soap/air interface . In the diagram on the left, there is a " $\pi$ " phase change at the corresponding location because the glass has a higher index than the soap film. This can make for significant differences observed when comparing the interference from two films of the same thickness.(The thickness of soap film for which rays 2 and 3 constructively interfere for a given wavelength of light will be different in the two cases.) The diagram on the right should also show some partial transmission at this point just like the diagram on the left has. (The amount of partial transmissions that occurs at this point is not exactly identical for the left and right cases, but that is a minor additional detail of secondary importance.) Note: In all 3 places labelled phase change, the phase change is precisely $\pi$. Note in each of these cases, the phase change is upon reflection, i.e. for the reflected portion of the wave. The transmitted portion of the wave never experiences any phase change. The reason the $\pi$ phase change occurs is the reflection coefficient $\rho$ for the E field at normal incidence is given by $\rho=(n1-n2)/(n1+n2)$. When n2>n1 the reflection coefficient has a "minus" sign which is a $\pi$ phase change necause $exp(i \pi)=-1$. (Alternatively $\cos(\omega t+\pi)=-\cos(\omega t)$ so that a "minus" sign multiplied on a wave amplitude is the same thing as a $\pi$ phase change.) For n1>n2 , the reflection coefficient is positive and no phase change occurs.

 

[EmilyBergendahl]

So as a viewer, assuming that the two soap films are of the same thickness, the interference patterns produced are different due to the fact that glass has a higher refractive index... Meaning that there is a phase change in case one and the resulting interference pattern is different than in case two.

 

[Charles Link]

So as a viewer, assuming that the two soap films are of the same thickness, the interference patterns produced are different due to the fact that glass has a higher refractive index... Meaning that there is a phase change in case one and the resulting interference pattern is different than in case two.

Yes. For very thin films, the glass case will even be reflective (rays 2 and 3 constructively interfere regardless of wavelength), whereas the very thin film in air will have cancellation in the rays 2 and 3 because of the single $\pi$ phase change (for ray 2). For thicker films, monochromatic light would have constructive interference for rays 2 and 3 in one case and have destructive (differ by $\pi$) in the other. Remember ray 3 gets an extra phase term that depends on the path length through the soap film and back. That coupled with any $\pi$ phase changes determines the relative phases of rays 2 and 3. Qualitatively, you can expect the two cases to appear very similar though, because it is difficult to control the thickness of the film. The films will vary in thickness in both cases and you can expect to see the kind of various color distributions that you see in soap films for either case.

 

[EmilyBergendahl]

Thank you Charles! Your help is appreciated so much!