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29) therefore becomes Dtot ¼ ya ðPa þ Pb À dPa Pb Þ: ð2:30Þ The power Ptot of the combination, defined as f2À1 where f2 is the principal image-side focal length, is Ptot ¼ Dtot =ya . The power of the pair of lenses separated by distance d is therefore Ptot ¼ Pa þ Pb À dPa Pb : ð2:31Þ The focal point can also be found geometrically from the figure, without recourse to tedious algebra. Note that the power of the combination is less than the sum of their individual powers, unless they are in contact, when the powers add directly.
These constitute the spherical aberration already described. Coma is a wavefront distortion additional to spherical aberration, which only appears for object points off-axis. 27). The typical comatic image consists of superposed circular images, successively shifted further from the axis and focused less sharply. Astigmatism is the result of a cylindrical wavefront aberration, which increases as the first power of r. The effect is unfortunately familiar in many human eyes, which show astigmatism even for objects on-axis.
The use of a lens as a simple magnifier, and the combination of optical components in systems such as the microscope and telescope, will be considered in the following chapter. 1 The Thin Prism The wavefront concept is usefully applied to the bending of a light ray in a prism, with apex angle a and refractive index n, assuming free space1 outside the prism. 4)) to each surface in turn, and find a useful approximation for a thin prism at near-normal incidence. We then show that the wavefront approach leads directly to this approximation.