A thick lens consists of two spherical surfaces with curvature R₁, R₂ separated by a thickness d of material of refractive index n. Show that the power P of the thick lens is given by P = P₁ + P₂ − (d/n) P₁P2 where P₁, P₂ are the powers of the two surfaces. (The argument of Section 2.7 does not work here. You can use instead the matrix algebra of Section 2.8.)

A thick lens consists of two spherical surfaces with curvature R₁, R₂ separated by a thickness d of material of refractive index n. Show that the power P of the thick lens is given by P = P₁ + P₂ − (d/n) P₁P2 where P₁, P₂ are the powers of the two surfaces. (The argument of Section 2.7 does not work here. You can use instead the matrix algebra of Section 2.8.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Applications Of Reflection Of Light

When a light ray (termed as the incident ray) hits a surface and bounces back (forms a reflected ray), the process of reflection of light has taken place.

Sign Convention for Mirrors

A mirror is made of glass that is coated with a metal amalgam on one side due to which the light ray incident on the surface undergoes reflection and not refraction.

Question

A thick lens consists of two spherical surfaces with curvature R₁, R₂ separated by a thickness d of material of
refractive index n. Show that the power P of the thick lens is given by P = P₁ + P₂ − (d/n) P₁P₂ where P₁, P2
are the powers of the two surfaces. (The argument of Section 2.7 does not work here. You can use instead the
matrix algebra of Section 2.8.)

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Step 1: Introduction:

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Step 2: consideration of thin lens:

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Step 3: Taking Matrixes:

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Step 4: After performing the matrix multiplication and simplification, we arrive at the expression:

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Step 5: Finally,

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