3. A lens is moved along the central axis between a fixed object and a fixed image screen. The object and image are separated by a distance L. Suppose L is more than four times the focal length of the lens. Now you found two positions of the lens for which an image is in focus on the screen; one case is magnified and another case is reduced. The distance between the two positions of the lens is D.

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Chapter1: Units, Trigonometry. And Vectors
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3.
A lens is moved along the central axis between a fixed object and a fixed image screen. The object and image are
separated by a distance L. Suppose L is more than four times the focal length of the lens. Now you found two
positions of the lens for which an image is in focus on the screen; one case is magnified and another case is
reduced. The distance between the two positions of the lens is D.
Object
Position 1
D
L> 4f
Position 2
Screen
(a) The distances to the object and the screen of the first position of the lens are s₁ and sí, respectively. The
distances to the object and the screen of the second positon of the lens are s₂ and s2, respectively. Find an
expression for f in terms of S₁, si and L.
(b) Find an expression for f in terms of S₂, s2 and L.
(c) Find an expression for f in terms of L and D, only.
Transcribed Image Text:3. A lens is moved along the central axis between a fixed object and a fixed image screen. The object and image are separated by a distance L. Suppose L is more than four times the focal length of the lens. Now you found two positions of the lens for which an image is in focus on the screen; one case is magnified and another case is reduced. The distance between the two positions of the lens is D. Object Position 1 D L> 4f Position 2 Screen (a) The distances to the object and the screen of the first position of the lens are s₁ and sí, respectively. The distances to the object and the screen of the second positon of the lens are s₂ and s2, respectively. Find an expression for f in terms of S₁, si and L. (b) Find an expression for f in terms of S₂, s2 and L. (c) Find an expression for f in terms of L and D, only.
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