Ch0228 - Chapter 28 Thin Lenses: Ray Tracing 28 Thin...

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Chapter 28 Thin Lenses: Ray Tracing 243 28 Thin Lenses: Ray Tracing A lens is a piece of transparent material whose surfaces have been shaped so that, when the lens is in another transparent material (call it medium 0), light traveling in medium 0, upon passing through the lens, is redirected to create an image of the light source. Medium 0 is typically air, and lenses are typically made of glass or plastic. In this chapter we focus on a particular class of lenses, a class known as thin spherical lenses. Each surface of a thin spherical lens is a tiny fraction of a spherical surface. For instance, consider the two spheres: A piece of glass in the shape of the intersection of these two spherical volumes would be a thin spherical lens. The intersection of two spherical surfaces is a circle. That circle would be the rim of the lens. Viewed face on, the outline of a thin spherical lens is a circle. The plane in which that circle lies is called the plane of the lens. Viewing the lens edge-on, the plane of the lens looks like a line. Lens The Plane of the Lens
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Chapter 28 Thin Lenses: Ray Tracing 244 Each surface of a thin spherical lens has a radius of curvature. The radius of curvature of a surface of a thin spherical lens is the radius of the sphere of which that surface is a part. Designating one surface of the lens as the front surface of the lens and one surface as the back surface, in the following diagram: we can identify R 1 as the radius of curvature of the front surface of the lens and R 2 as the radius of curvature of the back surface of the lens. The defining characteristic of a lens is a quantity called the focal length of the lens. At this point, I’m going to tell you how you can calculate a value for the focal length of a lens, based on the physical characteristics of the lens, before I even tell you what focal length means. (Don’t worry, though, we’ll get to the definition soon.) The lens-maker’s equation gives the reciprocal of the focal length in terms of the physical characteristics of the lens (and the medium in which the lens finds itself): The Lens-Maker’s Equation: + = 2 1 o 1 1 ) ( 1 R R n n f (28-1) where: is the focal length of the lens, n is the index of refraction of the material of which the lens is made, n o is the index of refraction of the medium surrounding the lens ( n o is typically 1 . 00 because the medium surrounding the lens is typically air), R 1 is the radius of curvature of one of the surfaces of the lens, and, R 2 is the radius of curvature of the other surface of the lens. R 2 R 1 The Front Surface of the Lens The Back Surface of the Lens
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Chapter 28 Thin Lenses: Ray Tracing 245 Before we move on from the lens-maker’s equation, I need to tell you about an algebraic sign convention for the R values. There are two kinds of spherical lens surfaces. One is the “curved out” kind possessed by any lens that is the intersection of two spheres. (This is the kind of lens
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Ch0228 - Chapter 28 Thin Lenses: Ray Tracing 28 Thin...

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