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$\bullet$$\bullet$ An oil tanker spills a large amount of oil $(n=1.45)$ intothe sea $(n=1.33)$ . (a) If you look down onto the oil spillfrom overhead, what predominant wavelength of light do yousee at a point where the oil is 380 nm thick? (b) In the waterunder the slick, what visible wavelength (as measured in air) ispredominant in the transmitted light at the same place in theslick as in part (a)?

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a) 441 nmb) 551 nm

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Simon Fraser University

Hope College

University of Sheffield

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.

04:20

$\bullet$$\bullet$ An oil …

06:17

35.58. An oil tanker spill…

03:09

An oil tanker spills large…

10:58

A disabled tanker leaks ke…

06:24

Leaking Tanker A disabled …

03:53

A thin layer of oil $(n=1.…

02:03

An oil tanker has collided…

01:34

Red light $(\lambda=630 \m…

05:48

(II) A thin film of oil $\…

01:07

A certain crude oil has an…

02:26

Visible light is incident …

03:31

01:48

02:55

A certain grade of crude o…

06:34

A sheet of glass is coated…

since the index of refraction of air is less than the index of refraction of oil, there's going to be a 183 phase shift on the first reflection from the air into the oil. When some of the light goes into the oil and then reflects off the water, there's not going to be a 180 degree spaceship because the index of refraction of water is actually less than that of oil, and so the net phase shift is 180 degrees. This means that the condition for a constructive interference is Tootie is equal to one plus 1/2. I was Landa. This is the constructive interference equation for this problem because there's into little 180 degree facial. So whenever you have this, you have to swap them t destructive in the construct of equation. So this is now the construct of equation. I was labeled by sea, and then the destructive equation is Tootie is equal to him, Landa, which is normally the construct of the question. And so let's do party now. We're concerned with the constructive interference at the top and so we have to t is equal to m plus 1/2 time's lambda. In this case, this is the lambda inside the oil. And so the land inside oil is related to the original Lambda by this equation. And so I'm going to substitute that in get film plus 1/2 lambda not over in now I'm going to solve her land and not and I get to the end over in plus 1/2 and then I can plug in everything that the problem gives me. So tea is 3 80 nana meters in his one point for five as he an exit a fraction of the oil you also have. And so this equals 1102 Nana meters over in plus one. Okay, Now we can start playing in values to figure out what the wavelengths are, and so for him is equal to zero. This ends up giving 22 100 nana meters for landing. Not for a musical one. The sense of giving 735 centimeters for him is equal to this gives 441 animators and then I'm going to Lhasa live here for Emma's equal to three. This gives Lambda Nana is equal to three fifteen 15 damn years. Now, this isn't This is outside the visible range. This is outside of his range and this is outside of his orange. And so this is the only one that we see here. And that completes part, eh? In part B. We're worried about the construct of equation. And the reason that is, is that the way of looks that are predominant for the transmitted light are those for which there is destructive interference for the reflected light. And so now we're worried about the construct of equation, which is Tootie is equal to em Landa and something here we're going to solve for Lambda. Not but first we're gonna plug in that land. Is Linda not over? And And so if you follow this somewhere, Lito, last time he'll get that Landon on is equal to to t n over l so student and values Here we get 1102 nanometers over him. Now start playin in values for M is equal to one. This gives us a lambda not of 1102 nanometers for M is equal to two. This gives us a lambda not of 551 centimeters for M is equal to three. This guy's a landing on 367. And so we're gonna eliminate these in these and focus on only the one that's in the visible range, which is this one right here. And so that is the lamb in on, and that completes the problem.

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