All Problems 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 \(d\) and curvature radii of the surfaces are the same and equal to \(R\); (b) whose refractive surfaces are concentric and have the curvature radii \(R_{1}\) and \(R_{2}\left(R_{2}>R_{1}\right)\).
5.59. (a) \(\Phi=d(n-1)^{2} / n R^{2}>0,\) the principal planes are located on the side of the convex surface at a distance of \(d\) from each other, with the front principal plane being removed from the convex surface of the lens by a distance of \(R /(n-1) ;(b) \Phi=\left(1 / R_{2}-1 / R_{1}\right) \times\) \(\times(n-1) / n<0 ;\) both principal planes pass through the common curvature centre of the surfaces of the lens.