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$\bullet$ If a diffraction grating produces a third-order bright spotfor red light (of wavelength 700 $\mathrm{nm}$ ) at $65.0^{\circ}$ from the centralmaximum, at what angle will the second-order bright spot befor violet light (of wavelength 400 $\mathrm{nm} ) ?$

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$20.2^{\circ}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

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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.

02:34

A diffraction grating has …

01:17

If a diffraction grating p…

02:53

01:25

At what angle will the sec…

01:14

Find the angle for the thi…

01:16

01:08

A diffraction grating with…

01:34

Oh, righty. So for this problem, we know the wavelength of our first situation to 700 Nana meters and that the third bright spot happens at 65 degrees and we want to know for that same grading for a way of length of 490 meters. At what angle? This is the second bright spot gonna be So we can use this information from our 1st 1 to figure out what the spacing between the sleds and our diffraction grating is using D signed data equals and lambda. So if we saw for D, you get t equals and Landa over sign data. So for this situation, if we pull in our numbers, this is the third border bright spot or a wavelength of 700 nanometers. Sign of 65 degrees gives us a slip spacing of 23 17.1 mana meters. Now I can do the same thing up here. This guy so decide Data sequel to End Landa. Now we're looking for Seita so sign data equals n lambda over Deep said Seita is the inverse sine m lambda over D. So if I play and my numbers now, we're dealing with the second spot and the new wave length of 400 nanometers and the slit spacing that we just solved for 23 17.1 indiana meters. Make sure your units are the same. Gives me, uh, they two of 20.22 groups.

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