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$\bullet$ A diffraction grating has 5580 lines/cm. When a beam ofmonochromatic light goes through it, the second pair of brightspots occurs at 26.3 $\mathrm{cm}$ from the central spot on a screen42.5 $\mathrm{cm}$ past the grating. (a) What is the wavelength of thislight? (b) How far from the central spot does the next pair ofbright spots occur on the screen?

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a) 471.5 nmb) 54.6125 cm

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

University of Sheffield

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.

06:45

A diffraction grating has …

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When laser light of wavele…

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$\bullet$ When laser light…

01:35

A red laser pointer with a…

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If blue light of wavelengt…

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okey dokey on this problem. We have a diffraction grating that's 55 80 lines. Her centimeter. We know that the second bright spot, some would call that Why, too, occurs at 26 0.3 centimeters away from the central bright spot. And we know that the screen is the distance of 42.5 centimeters away. We want to know what is the wavelength of the light that's going through that grading. And then what's the distance from the centre right spot to the third bright spots? So, no. In this case, unlike we've been dealing with for a lot of our diffraction problems, the wide distances and are are very similar to each other. So these really big angles, so we can't use the assumption that sign data is approximately Tan data is approximately Seita. That's not valid here. So we need to actually go in and look at what are the eagle's gonna be. So this is my diffraction grating on my screen is over here. This is our You have a bright spot. One for its body. All right, spot, right spot. So my second bright spot. Why two It's going to make an angle being too. So the tangent of the ankle is opposite over Jason. So that's why, too, over our so say, uh, it's just the inverse tangent fly to overlook. So now we can use that with our bright spot equation d sign data. It's equal to end landa. So if I plug in for Seita, we got d sign of inverse T engine. Well, I tiu over our I like to leave things symbolic for everything personally, just cause it helps mitigate rounding errors. Okay, so we're looking for Lambda first so that you just need to divide all this by M. And that gives us our equation for Lando. So let's hop over to another page. All right? So where we left off, he said that Lamba was evil to d sign of inverse tangent. Why over our all divided by Yeah, Okay, so if I plug in of my numbers D is the reciprocal of the like lines, percent immunity, whatever. So, for every one centimeter, there are 55 Katie, once Senator says how the unit of a distance now. So it's a the wits of our slicks and our greeting sign of inverse tangent. Now, Why, too, was given as 26.3 centimeters and are the distance to my screen was 42.5 centimeters divided by and which is to cause the second French. Make sure that your units are the same. So I have centimeters over centimeters unit, less quantity inside my tan and my sign, That's great. So I'm gonna end up getting my lambda in units of centimeters out here. So when I plug that into my handy dandy calculator, that gives me a lambda of 4.715 times 10 to the negative five centimeters, which is the same as 4 71 point five nana meters. So it's nice. And in that simple spectrum already, So that's part a. So now we want to know where is that third breakthrough is gonna be? So now we just need to work backwards. That's Papa. Been a new page. So we know the bright spots happened at D. Sign data equals and Lambda simply sold for Seita. Signed data equals M lambda over D. Since data is the inverse side of n lambda over tea, and then from there we can use the same relationship that 10th data. That's why over our So why this our tea and data? So let's put them together. I'm gonna take this data. Shove it in there. So why is equal toe are t engine of inverse sine only under over deep Now we want to do this for m equals three. So are the distance to my screen was 42.5 centimeters tangent in first sign. Uh, serene times Landa. So my d we have in centimeters. It was one of those air, I guess One centimeter over 55 80 lines. So I'm gonna use the wavelength That was centimetres just so I don't have to convert that because I don't want to. So 4.715 times 10 to the negative Five centimeters Shoop Shoot! So I have centimeters. Cancel. That was centimeters unit lists. We'll end with units of centimeters. So why three is equal to you? 54.63 centimeters

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