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Photometry and Geometrical Optics

Problem 5.54

A telephoto lens consists of two thin lenses, the front converging lens and the rear diverging lens with optical powers Φ1=\Phi_{1}= =+10D=+10 \mathrm{D} and Φ2=−10D\Phi_{2}=-10 \mathrm{D}. Find: (a) the focal length and the positions of principal axes of that system if the lenses are separated by a distance d=4.0 cmd=4.0 \mathrm{~cm} (b) the distance dd between the lenses at which the ratio of a focal length ff of the system to a distance ll between the converging lens and the rear principal focal point is the highest. What is this ratio equal to?

Reveal Answer
5.54.5.54 . (a) The optical power of the system is Φ=Φ1+Φ2−\Phi=\Phi_{1}+\Phi_{2}- −dΦ1Φ2=+4D,-d \Phi_{1} \Phi_{2}=+4 \mathrm{D}, the focal length is 25 cm.25 \mathrm{~cm} . Both principal planes are located in front of the converging lens: the front one at a distance of 10 cm10 \mathrm{~cm} from the converging lens, and the rear one at a distance of 10 cm10 \mathrm{~cm} from the diverging lens (x=dΦ2/Φ\left(x=d \Phi_{2} / \Phi\right. and x′=−dΦ1/Φ)\left.x^{\prime}=-d \Phi_{1} / \Phi\right) (b) d=5 cm;d=5 \mathrm{~cm} ; about 4/34 / 3
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