giving from (2.16)
For ray r2, with the same height y, we have
Eqs. (2.18) and (2.19) give nn f = - f , or, for a system in a vacuum (or air, as a normal approximation)
The quantity n/f in Eq. (2.20) is called the 'power of the optical system and is often denoted by K. The reciprocal of K is the equivalent focal length and is, in a vacuum (or air as approximation), given by f = -f. Eq. (2.7) can then, from Eq. (2.20), be written in the general form n n n
Figure 2.5 illustrates the derivation of what is probably the most fundamental law of Gaussian optics, in that it is related to the first law of thermodynamics because it governs the energy throughput of optical systems. This is the Lagrange Invariant (also known, variously, as the Smith, Lagrange, Helmholtz relationship).
The transverse magnification m of the system is given by n /n where the object and image points I and I on axis are conjugate and Ih and Ih at height n and n respectively. From Eq. (2.9)
n sf while from Eq. (2.22) and Fig. 2.5 with optical distances s /n and s/n n ns
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