?(a) Derive Equation 3 for Gaussian optics from Equation 1 by approximating \(\cos
Chapter 11, Problem 34(choose chapter or problem)
(a) Derive Equation 3 for Gaussian optics from Equation 1 by approximating \(\cos \phi\) in Equation 2 by its first-degree Taylor polynomial.
(b) Show that if \(\cos \phi\) is replaced by its third-degree Taylor polynomial in Equation 2, then Equation 1 becomes Equation 4 for third-order optics.
[Hint: Use the first two terms in the binomial series for \(\ell_{0}^{-1}\) and \(\ell_{0}^{-1}\). Also, use \(\phi \approx \sin \phi\)]
Equation Transcription:
𝜙
𝜙
ℓ
ℓ
𝜙 𝜙
Text Transcription:
cos phi
cos phi
l ^-1 _0
l ^-1 _i
phi approx sin phi
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