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. Dental mirror. A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect image with a magnification of 2.00 when the mirror is 1.25 $\mathrm{cm}$ from a tooth. (Treat this problem as though the object and image lie along a straight line.) (a) What kind of mirror (concave or convex) is needed? Use a ray diagram todecide, without performing any calculations. (b) What must be the focal length and radius of curvature of this mirror? (c) Draw a principal-ray diagram to check your answer inpart (b).

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It is a concave mirror with radius 5 $\mathrm{cm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

University of Washington

Hope College

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.

04:27

A dentist uses a curved mi…

04:00

06:38

01:14

03:34

05:33

06:10

A dentist uses a spherical…

01:50

A dentist uses a mirror to…

02:17

A dentist's mirror pr…

our were given an image, but we want an image that is direct and magnified. So let's start off. Let's start off with this equation here. I wanna rest image distance. Plus, one object is since it's one of her ass crime which distance? People's one ever f foc elect. So we can rearrange this. This is, uh, in terms of s prime one arrest prime people's ref, and then you do some algebra to get it in the form as prime equals s times off over. So from there, we know that. Well, we know the magnification is negative s fire of sa we something to that into magnification equation. Where we get is magnification equals negative. Over s minus half. Okay, um and so for so for a cull. Vicks mirror, you have, uh, that ask is negative. So negative f would just be the absolute value, Beth. All right, so basically, you you're magnification equation reduces to m equals absolute value over s plus absolute very best. And as you can see, the denominators creator, the numerator some magnification is less than warm. The convex case. This implies that this must be a con cave mirror to produce the magnification off plus two. Okay, so that's part a on part B will actually work out some values. So m is negative es over us making best prime over us. So we know as we know them. So s prime will be negative. M times s so that would be negative. Two times 1.25 centimeters, which is our object distance for the mayor. And so the image distance from the mirrors to print five cent of use negative 2.5 centimeters. So 2.5 centimeters to the opposite side of the mirror as the object is right on part B or rather, continuing part B we now want. So we have as prime we want the focal. And for that, we go back to, uh, this equation. Here are this equation here. Eso won over f I would be recalled, Tio one arrest prime plus one of us. So that's negative. One over 2.5, as we've just found, plus one over 2.5. So this implies that s will be 2.5 centimeters. Uh, since this is a come cave mirror, uh, R will be twice that of us and so that would be two times 2.5. And so radius of curvature is five centimeters. All right, But all of this, we now have we not know that we have a magnified image that is correct. And a CE prime is negative. Meaning it is virtual so river virtual direct, magnified image. So, um, Alice, look at the red eye from on dso here F is the focal point. Cia's the curvature, points of races, cultures twice that of efforts you can see here. Oh, here is the object distance that's about half their greatest off. That's about half the focal length. 1.2 for this 1.2 1 to 5. Your image distance is 2.5 and note that the image is magnified. So it is vertically higher than the object. And it is virtual meeting us on the other side of the mirror. Asked the cock. It mirrors the object. And it is. It is also direct, meaning it is on the same side off the of access as yet. So I've John for Ray's with black are blue, red and green to show the four different race from the principal of a diagram and By the way, this is all this committee all found in section 24.3 in the book, which doesn't really good job of highlight ofthe giving you the recipe for joining one of these things. So So, first of all, we make sure that the the sort of scales are least roughly accurate. And then we just four ways that converge on the other side of the mirror as the object. So that's that point then. That is where we will see the image. So rain one is the ray going parallel to the access. It's kind of hidden behind all these other rays here. But Ray one is actually this black line goes over here, bounces back down, but the virtual But the the reflection on the other side of the mirror goes to the virtual image of conversions here similarly for merch. Too far away to you have you have Ah, rain. That is going. But ah, that is going up in a pawn bouncing off of the mirror Will will be will be parallel to the access and the reflection on your side will meet to get the conversion point. Very three is going to the curvature that's bouncing and going to the curvature. But the other side eyes meeting at the conversions point. Finally, Ray for On Green is going of is bouncing off of the Vertex of the mirror and bouncing off symmetrically, and the extension behind that ray will converge at the point of the image that is it.

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