(a) Derive Equation 3 for Gaussian optics from Equation 1 by approximating cos in Equation 2 by its first degree Taylor polynomial (b) Show that if cos is replaced by its third degree Taylor polynomial in Equation 2, then Equation 1 becomes Equation 4 for third order optics ...

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(a) Derive Equation 3 for Gaussian optics from Equation 1 by approximating cos in Equation 2 by...

Question:

(a) Derive Equation 3 for Gaussian optics from Equation 1 by approximating cos Φ in Equation 2 by its first-degree Taylor polynomial.
(b) Show that if cos Φ is replaced by its third-degree Taylor polynomial in Equation 2, then Equation 1 becomes Equation 4 for third-order optics.