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Photometry and Geometrical Optics

Problem 5.59

Find the positions of the principal planes, the focal length and the sign of the optical power of a thick convex-concave glass lens (a) whose thickness is equal to dd and curvature radii of the surfaces are the same and equal to RR; (b) whose refractive surfaces are concentric and have the curvature radii R1R_{1} and R2(R2>R1)R_{2}\left(R_{2}>R_{1}\right).

Reveal Answer
5.59. (a) Φ=d(n−1)2/nR2>0,\Phi=d(n-1)^{2} / n R^{2}>0, the principal planes are located on the side of the convex surface at a distance of dd from each other, with the front principal plane being removed from the convex surface of the lens by a distance of R/(n−1);(b)Φ=(1/R2−1/R1)×R /(n-1) ;(b) \Phi=\left(1 / R_{2}-1 / R_{1}\right) \times ×(n−1)/n<0;\times(n-1) / n<0 ; both principal planes pass through the common curvature centre of the surfaces of the lens.
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