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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 n0=1.7n_{0}=1.7 if its optical power in air is Φ0=−5.0D\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 Φ0=+10D\Phi_{0}=+10 \mathrm{D}

Reveal Answer
5.33.(a)Φ=Φ0(n−n0)/(n−1)=2.0D,f′=−f=n0/Φ==85 cm;(b)Φ=1/2Φ0(2n−n0−1)/(n−1)=6.7D,f= \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/Φ≈15 cm.f′=n0/Φ≈20 cm.=1 / \Phi \approx 15 \mathrm{~cm} . f^{\prime}=n_{0} / \Phi \approx 20 \mathrm{~cm} . Here nn and n0n_{0} are the refrac- tive indices of glass and water.
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