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Unformatted text preview: Physics 54 Lenses and Mirrors And now for the sequence of events, in no particular order. Dan Rather Overview We will now study transmission of light energy in the ray approximation , which assumes that the energy travels in straight lines except when there is reFection, refraction., or interception by an obstacle. This approximation works well when the sizes of apertures and obstacles are large compared to the wavelength of the light. Our main interest will be in formation of images by lenses and mirrors. We will also study the use of these in simple optical instruments. The lenses and mirrors will generally be assumed to have either plane or spherical surfaces. This simplies the geometry. or the most part, we will further assume that the rays of light make small angles with the symmetry axis of the device. This paraxial ray approximation allows derivation of simple formulas for locating and describing images. inally, we will assume that the indices of refraction of lenses are independent of the wavelength of light, ignoring the effects of dispersion . Some "aberrations" that arise from violations of these approximations will be discussed. Mirrors We consider mirrors made of a conducting material (so the reFection is essentially 100%) in the shape of part of a sphere. If the mirror surface is concave, the mirror is called converging or "positive" (for reasons to be made clear); if the surface is convex, the mirror is called diverging or "negative". Consider rst a concave mirror, shown in a side view. The line along the sphere's diameter is the symmetry axis. We consider two incident rays, parallel to the axis and close to it, so the angles involved in the reFection are small. Point C is the center of the spherical surface, which has radius R. After reFection the two rays cross each other at a point on the axis. This is the focal point of the mirror. Its distance f from the mirror (the focal length ) is obtained by some simple geometric arguments. Axis C f d PHY 54 1 Lenses and Mirrors The two right triangles with opposite side d give (using the paraxial ray assumption that both angles are small) tan = d / R , tan = d / f The angle of reFection is equal to the angle of incidence , so = 2 . Thus we nd a simple formula for f : ocal length of a mirror f = R /2 In this case the parallel rays converge to a focus, which is why the mirror is called converging. Its radius R and its focal length f are assigned positive values in this case, which is why it is also called a positive mirror. Next consider a convex mirror, as shown. The center of the sphere is on the side opposite to that where the light impinges and is reFected....
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