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$\cdot$ The front, convex, surface of a lens made for eyeglasses has a radius of curvature of $11.8 \mathrm{cm},$ and the back, concave, surface has a radius of curvature of 6.80 $\mathrm{cm} .$ The index of refraction of the plastic lens material is 1.67 . Calculate the local length of the lens.

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$-23.95 \mathrm{cm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 24

Geometric Optics

Electromagnetic Waves

Reflection and Refraction of Light

University of Michigan - Ann Arbor

University of Washington

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.

03:39

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00:27

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Okay. We use the thin lens equation, which can be stated as one of the focal anti equals, uh, refractive index minus one times one of where this of curvature one minus one of the radius of curvature too. And this is for the front end being come being convex and the back end being Kong cave. Okay, Um can cave back cutbacks front. And that is exactly what the situation Ah, that sets us up wit in this problem. So we're good to go in terms of our warning there, too. We know. And is 1.67 You write that down on this one. Times one over 11.8 centimetres, minus one over 6.8 centimetres. Noticed that this sign were changed. Thes signs would change depending on whether or not ah, they're convex or concave ends. But we're good in this case and on. So this works out to be 0.67 times uh, negative print. Oh, 6 to 3, etcetera, etcetera. And so you get eventually that I have folk. That focal length is negative. 27. Ah, negative. 24 centimeters.

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