∙The walls of a soap bubble have about the same index of refraction as that of plain water, n=1.

step 1 Alrighty. So in this problem, we have a soap bubble. We're just going to zoom in on the soap bub

∙The walls of a soap bubble have about the same index of...

Key Concepts

Visible Spectrum

The visible spectrum comprises the range of wavelengths of light that can be detected by the human eye, typically from about 380 nm to 750 nm. Different wavelengths within this range correspond to different colors. In problems involving thin film interference, predicting which wavelength is most strongly reflected allows one to identify the resultant color observed, as each wavelength falls into a specific region of the visible spectrum.

Thin Film Interference

Thin film interference is an optical phenomenon that occurs when light waves reflect off the two surfaces of a thin layer of material and then interfere with each other. This interference can enhance or diminish certain wavelengths of light based on the film's thickness, the light’s wavelength, and the refractive indices involved, leading to colorful patterns seen in soap bubbles and oil films.

Optical Path Difference

The optical path difference is the difference in the distance traveled, multiplied by the refractive index, by two light waves taking different paths. In thin films, it is the extra distance traveled by light reflecting off the bottom surface compared to the top surface. This difference determines whether the reflected light waves will interfere constructively or destructively, which depends on the film thickness and the light’s wavelength.

Phase Change upon Reflection

Phase change upon reflection refers to the shift in the phase of a light wave that can occur when light reflects off an interface between media with different refractive indices. Specifically, when light reflects from a medium of higher refractive index, it undergoes a half-wavelength (or 180°) phase shift. This phase change is critical in determining the conditions for constructive or destructive interference in thin films.

Constructive Interference Condition

The condition for constructive interference in a thin film is achieved when the optical path difference, taking into account any phase shifts upon reflection, results in the reflected waves being in phase. This typically involves setting the optical path difference equal to an integer multiple of the wavelength (or half-wavelengths if a phase shift occurs) so that the peaks of the light waves align, thus enhancing the reflection of specific wavelengths.

Refractive Index

The refractive index is a measure of how much the speed of light is reduced inside a medium compared to its speed in vacuum. It not only affects the wavelength of light within the material but also plays a crucial role in determining the degree of refraction and phase shifts upon reflection. In contexts such as soap bubble walls, the refractive index helps define the optical path length and thus influences the interference pattern.

Transcript

00:03 Alrighty.

00:05 So in this problem, we have a soap bubble.

00:11 We're just going to zoom in on the soap bubble wall real nice and close.

00:19 So we're shining light into our soap bubble from air, which has an index of refraction of one.

00:28 There's air inside of it.

00:31 And then the wall of our soap bubble has an index of refraction of 1 .33.

00:39 Now, if you're thinking, out exactly what we're doing, we need to take a second to draw all of our beautiful light paths.

00:48 So when we have our light coming in, when it hits this surface, it's going to be partially reflected there, and then partially transmitted, and then get reflected here and come back out.

01:14 So there's two important parts in this process.

01:17 When we get a reflection here and when we get a reflection here.

01:23 So at this first junction, when we're bouncing here, we're going from an index of refraction 1 to an index of refraction 1 .33.

01:36 So when you go from a smaller index of refraction and reflect off of a higher index of refraction, that's going to give you a phase shift of half of a cycle.

01:53 And when down here we come from a higher index of a fraction and reflect off of a lower one, there's no phase shift.

02:07 So this throws our two beams that get reflected out of the soap bubble out of phase by 180.

02:15 So if we're going to view this reflection with our eyeballs, we're going to be viewing the constructive interference.

02:26 Because if it's destructive, we're not going to see it.

02:28 It's going to be a nice dark spot.

02:32 But remember from the section two sections ago, 26 .1, if the two beams are out of phase, your constructive interference occurs at half integer values.

02:50 So when we're talking about our thin films, the relationship here between m lambda and our thin films is m plus a half, because they're out of phase, lambda of the film, so i'm going to put a little f there, is equal to two times the thickness of our thin film.

03:17 So a thing to specify here is that this is the thickness of our thin film.

03:27 Cool.

03:28 So all of our phase shift business is happening in here, and we're getting the path length different.

03:36 Which allows for constructive and destructive interference from traveling twice this thickness.

03:44 So that's where the two t comes from because our path link is being thrown off by one t, 2t, and then it's going back out.

03:55 All right.

03:56 So now the other important thing to note that they don't really describe super clearly in the book is that this wavelength is the wavelength inside the film because this.

04:07 That's where this shifting is occurring.

04:11 So inside the film, i have an index of refraction that is not equal to one...

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