Download PDF by Albert G. Ingalls: Amateur Telescope Making Vol 3

By Albert G. Ingalls

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Index given at r = 0°C, pressure = 760 mm Hg, water vapor pressure = 4 mm Hg. b. ATMOSPHERIC TURBULENCE The assumption that n = n(z) neglects variations in index that are present in a turbulent atmosphere at constant height due primarily to temperature fluctuations. Consider a ray that enters the atmosphere from directly overhead, with the deviation of the ray from a vertical path denoted by a. Assuming a <^ 1 we can write Eq. 4) where the term in sin a is dropped because a is small. Letting n = \ + dn, Eq.

Conic Sections 41 which can be rewritten as / + 2z z2-r = 0. 7) agree if we choose b^ = —ss\ and 2a = s -\- s\ As before, the replacement of 3;^ by x^ +7^ gives a hyperboloid of revolution about the z-axis. The case of a convex mirror with one conjugate at infinity is left as an exercise for the reader. The appropriate surface for this situation is a paraboloid. 5. CONIC SECTIONS Each of the surface cross sections derived in the preceding section is a conic section and it is therefore appropriate to find a single equation describing the family of such curves with the vertex at the origin.

A thick plate is a good example of a simple system with aberration, that is, it fails to take all rays from a single object point into a single image point. This is easily shown by applying Snell's law in its exact form at each surface. With the intermediate steps left to the reader, the geometry of Fig. 6) A comparison of Eqs. 7) n/=n2=n Fig. 6. Image shift A for plane-parallel plate of thickness d and index n in air. See Eqs. 7) for discussion. 5. Two-Mirror Telescopes 17 hence the image position depends on the ray height at the first surface.

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Amateur Telescope Making Vol 3 by Albert G. Ingalls

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