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$\bullet$$\bullet$ Suppose you illuminate two thin slits by monochromaticcoherent light in air and find that they produce their first inter-ference minima at $\pm 35.20^{\circ}$ on either side of the central brightspot. You then immerse these slits in a transparent liquid andilluminate them with the same light. Now you find that the firstminima occur at $19.46^{\circ}$ instead. What is the index of refrac-tion of this liquid?

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1.73

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

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.

03:27

Suppose you illuminate two…

03:29

35. 41. Suppose you illumi…

02:39

01:37

Two thin parallel slits ar…

01:48

A thin slit illuminated by…

02:35

Measuring Refractive Index…

02:55

Suppose you viewed the lig…

02:49

Light falls on two slits s…

Okay, No case on this problem. We have a double slit diffraction where the angle of the first minimum, that is plus or minus 35.20 degrees. Then we take that same diffraction grating on that same source of light, and we stick it in a transparent fluid. And now the angle of the first minimum was at 19.46 degrees. So this is initial. This is final. We're gonna say that and we want to find out what is the index of refraction of these things. So when we're sticking a light source into a transparent material, the thing that's changing this the wavelength of the light. So we want to focus on what's the wavelength of the light in both of these situations? Well, we know that we're dealing with two slit diffraction, and that's given to us by D Sign data is equal to, and it's the minimal we're looking at. So it's n plus 1/2 times Landa. So if I saw that for Lambda get D signed data over and was 1/2 Likewise, I also know that the index of refraction can be found from wavelengths by using the wavelength in air work divided by the wavelength in the material. So when he was a combination of these two things So if I use my equation for land on a stick it in here in air, I have d That's the distance between my slits. That's not changed. You raising the same grading sign. We're just gonna say it. Say it a initial here just to make it clear. Over and plus 1/2 all over D. Same grading so still D signed data final over in plus 1/2. Well, double dumb for fractions. How I hate does so our m plus a halves cancel my D's canceled and we're left with signe say, the initial divided by sign in the final. So the spacing of the slits and which interference pattern it was because we're looking at the same one doesn't actually matter. Only thing that matters is those difference in the angles. So butt plug in the Eagles signed. My initial angle was 35.20 degrees over sign 19.46 degrees. I get an index of refraction off 1.73

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