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$\bullet$ When laser light of wavelength 632.8 nm passes through adiffraction grating, the first bright spots occur at $\pm 17.8^{\circ}$ fromthe central maximum. (a) What is the line density (in lines/cm)of this grating? (b) How many additional bright spots are therebeyond the first bright spots, and at what angles do they occur?

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a) 4831 lines/cmb) $\pm 37.7^{\circ}$, $\pm 66.5^{\circ}$

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

Simon Fraser University

Hope College

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.

06:32

When laser light of wavele…

01:29

05:21

A laser beam of unknown wa…

03:21

$\bullet$ A laser beam of …

07:52

$\bullet$ A diffraction gr…

06:45

A diffraction grating has …

04:35

Three discrete spectral li…

02:16

02:53

Light at 633 nm from a hel…

04:23

Light of wavelength $631 \…

00:45

(II) A He-Ne gas laser whi…

01:50

Red laser light $(\lambda=…

00:38

When we use the diffraction grating, the bright spots are located at places that abide by this law. Here, thes signed data is equal to em. Lambda for part A. We're looking at the first maximum so and was going to be a little one. And we ultimately want to sell for D since D we can use to get the line density of the diffraction grating. It's a song for Dig is l'm Landa over science data like that, we're told the angle we know the wavelength and for the first maximum man was one. So's the land oversight there. And then now I can plug in things that they give us a problem. When we do that, we get that de is to 0.7 times 10 to the minus six meters, and we're going to convert this and the centimeters before we take the line density because they do want the line density in lines per centimeter. And so this is also equal to 2.7 times 10 to the mice for centimetres. Now the line density, which I'll just call ld for now line Dancy is equal to one over D, and so If we take the inverse of this, we get that. The line density is 4,830 lines. Personal vigor. And so this is the answer to party in part B. Want the rest of the angles associate with maximum, this diffraction grating. And so we're just going to use this law here. It's the same one that ruin the Ossa page under solving for sine data and land already. Now we sell for D in the previous part. We know Atlanta is, and we can substitute in different values of elm until we reach a maximum of data. And so, just pointing in line. Mandy, I get 0.3057 times l and now radio plugging in values for it was equal to plus surmise, too. This gives I fade. A is equal to plus or minus 37.7 degrees. When you take the inverse sign, you're going to get your answer and radiance. To get this answer here, you have to convert into degrees for Emma's equal to plus or minus three. I get us data of plus or minus 66.5 degrees, and that's the last one because once you go Hye Mi go past 90 that's not allowed. You won't see that bright spot ever. And so this is it.

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