All Problems Photometry and Geometrical Optics
Problem 5.50
Find the positions of the principal planes, the focal and nodal points of a thin biconvex symmetric glass lens with curvature radius of its surfaces equal to \(R=7.50 \mathrm{~cm} .\) There is air on one side of the lens and water on the other.
5.50. The principal planes coincide with the centre of the lens. The focal lengths in air and water: \(f=-1 / \Phi=-11 \mathrm{~cm}, f^{\prime}=\) \(=n_{0} / \Phi=+15 \mathrm{~cm} .\) Here \(\Phi=\left(2 n-n_{0}-1\right) / R,\) where \(n\) and \(n_{0}\) are the refractive indices of glass and water. The nodal points coincide and are located in water at the distance \(x=f^{\prime}+f=3.7 \mathrm{~cm}\) from the lens.