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$\bullet$ What is the thinnest soap film (excluding the case of zerothickness) that appears black when viewed by reflected lightwith a wavelength of 480 $\mathrm{nm}$ ? The index of refraction of thefilm is $1.33,$ and there is air on both sides of the film.

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180.5 nm

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

University of Michigan - Ann Arbor

Simon Fraser University

McMaster University

Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

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What is the thinnest soap …

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35.36. What is the thinnes…

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White light is incident on…

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(II) What is the smallest …

Soap Film Two The reflecti…

There is air on both sides…

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A soap film has an index o…

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A thin film of soap soluti…

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A soap film surrounded by …

in this prom, we're told that the surface of the film appears black, which means that there's destructive interference here. Sophie Imaginable wave coming up. If it reflects off a denser medium as this is here, then there's going to be 1/2 phase shift on the reflected wave. But the part that goes through and then is reflected on the other side is gonna have no face ships associated with it. In cases like these, this equation here describes the maximum or minimum. In this case, it's the minimum. So this describes the minimum and so really, we want to sell for the thickness of this, which is labelled by tea here. And we know the wavelength on the outside is 480 centimeters. But we don't know what it is on the inside. We know it will be different because the index of refraction changes here. But the index of refraction inside is 1.49 with the index of refraction here on the outside is one. And so it's all this equation for tea that's really are unknown. And so we get in Lambda over too. But we don't know Landa, but we do know Lambda Non. And we know the index of refraction and the two are related by this formula. And so playing this into here gives Elma Lambda knot or two in, and now we are just gonna let lb zero r one rather, we're going to be one. And so we have this and we know both these values they're given in the problem. So this is for any Nana meters. This is too. And units, refraction is one point 33 So I think I so I can't my notes wrong, Master B 1.33 there and this equals 80.5 nanometers. So this is the thickness of this film in order to get destructive interference for this land tonight and this index of refraction

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