All Problems Photometry and Geometrical Optics
Problem 5.33
Find the optical power and the focal lengths (a) of a thin glass lens in liquid with refractive index \(n_{0}=1.7\) if its optical power in air is \(\Phi_{0}=-5.0 \mathrm{D}\) (b) of a thin symmetrical biconvex glass lens, with air on one side and water on the other side, if the optical power of that lens in air is \(\Phi_{0}=+10 \mathrm{D}\)
\[ \begin{array}{r} 5.33 .(a) \Phi=\Phi_{0}\left(n-n_{0}\right) /(n-1)=2.0 \mathrm{D}, f^{\prime}=-f=n_{0} / \Phi= \\ =85 \mathrm{~cm} ; \quad(\mathrm{b}) \quad \Phi=1 / 2 \Phi_{0}\left(2 n-n_{0}-1\right) /(n-1)=6.7 \mathrm{D}, \quad f= \end{array} \] \(=1 / \Phi \approx 15 \mathrm{~cm} . f^{\prime}=n_{0} / \Phi \approx 20 \mathrm{~cm} .\) Here \(n\) and \(n_{0}\) are the refrac- tive indices of glass and water.