9. The following matrix product is used in discussing a thick lens in air: = (₁ (n-1)/R₂) - 1)/R²) (d/n 1) (1 - (n-1)/R¹), A = where d is the thickness of the lens, n is its index of refraction, and R₁ and R₂ are the radii of curvature of the lens surfaces. It can be shown that element A12 of A is -1/f where f is the focal length of the lens. Evaluate A and det A (which should equal 1) and find 1/f. [See Am. J. Phys. 48, 397-399 (1980).]

9. The following matrix product is used in discussing a thick lens in air: = (₁ (n-1)/R₂) - 1)/R²) (d/n 1) (1 - (n-1)/R¹), A = where d is the thickness of the lens, n is its index of refraction, and R₁ and R₂ are the radii of curvature of the lens surfaces. It can be shown that element A12 of A is -1/f where f is the focal length of the lens. Evaluate A and det A (which should equal 1) and find 1/f. [See Am. J. Phys. 48, 397-399 (1980).]