Chapter 3.15, Problem 9MP

The following matrix product is used in discussing a thick lens in air: $A=\left(\begin{array}{cc}1& \left(n-1\right)/R_2\\ 0& 1\end{array}\right)\left(\begin{array}{cc}1& 0\\ d/n& 1\end{array}\right)\left(\begin{array}{cc}1& -\left(n-1\right)/R_1\\ 0& 1\end{array}\right),$ where d is the thickness of the lens, n is its index of refraction, and $R_1$ and $R_2$ are the radii of curvature of the lens surfaces. It can be shown that element $A_{12}$ of A is $-1/f$ where f is the focal length of the lens. Evaluate A and detA (which should equal 1) and find $1/f.$ [See Am. J. Phys. 48, $397-399\left(1980\right).]$