To determine Part (a)To Show: The formula of focal length of combination of two thin lenses is represented by f T = f 1 f 2 / ( f 1 + f 2 ) Explanation Given: focal length of two lenses f 1 and f 2 , combined focal length f and combined power P, and power of both the lenses P 1 and P 2 . Formula used: lens formula for focal length 1 / f = 1 / v – 1 / u Calculation: If two thin lenses of focal length f 1 and f 2 are placed in contact with each other both on same principle axis as shown in diagram If a point object is placed on the principle axis at a distance u from the first lens L 1 . Its image would be formed by lens L 1 at I' at a distance v' from lens L 1 . Then, from the lens formula, we have 1 / v ' – 1 / u = 1 / f 1 … … … … . ( 1 ) I' will be used as a virtual object for second lens L 2 which forms a final image I at a distance v from it. Then, we have 1 / v − 1 / v ' = 1 / f 2 … … … … .. ( 2 ) From equation (1)and (2)by adding it we get 1 / v – 1 / u = 1 / f 1 + 1 / f 2 … … … … ... To determine Part (b)To Show: power of combination of lenses is equal to the sum of their separate powers, P = P 1 + P 2 .

7th Edition

ISBN: 9780321733627

Author: Douglas C. Giancoli

Publisher: PEARSON

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Chapter 23, Problem 87GP

To determine

Part (a)To Show:

The formula of focal length of combination of two thin lenses is represented by $f_{T} = f_{1} f_{2} / (f_{1} + f_{2})$

To determine

Part (b)To Show:

power of combination of lenses is equal to the sum of their separate powers, $P = P_{1} + P_{2}$ _.

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Chapter 23, Problem 86GP

Chapter 23, Problem 88GP

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Chapter 23 Solutions

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Part (a)To Show: The formula of focal length of combination of two thin lenses is represented by f T = f 1 f 2 / ( f 1 + f 2 )