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Photometry and Geometrical Optics

Problem 5.55

Calculate the positions of the principal planes and focal points of a thick convex-concave glass lens if the curvature radius of the convex surface is equal to R1=10.0 cmR_{1}=10.0 \mathrm{~cm} and of the concave surface to R2=5.0 cmR_{2}=5.0 \mathrm{~cm} and the lens thickness is d=3.0 cm.d=3.0 \mathrm{~cm} .

Reveal Answer
5.55. The optical power of the given lens is Φ=Φ1+Φ2\Phi=\Phi_{1}+\Phi_{2} −(d/n)Φ1Φ2,x=dΦ2/nΦ=5.0 cm,x′=−dΦ1/nΦ=2.5 cm-(d / n) \Phi_{1} \Phi_{2}, x=d \Phi_{2} / n \Phi=5.0 \mathrm{~cm}, x^{\prime}=-d \Phi_{1} / n \Phi=2.5 \mathrm{~cm} i.e. both principal planes are located outside the lens from the side of its convex surface.
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