
Concept explainers
A zoom lens system is a combination of lenses that produces a variable magnification of a fixed object as it maintains a fixed image position. The magnification is varied by moving one or more lenses along the axis. Multiple lenses are used in practice, but the effect of zooming in on an object can be demonstrated with a simple two-lens system. An object, two converging lenses, and a screen are mounted on an optical bench. Lens 1, which is to the right of the object, has a focal length of f1 = 5.00 cm, and lens 2, which is to the right of the first lens, has a focal length of f2 = 10.0 cm. The screen is to the right of lens 2. Initially, an object is situated at a distance of 7.50 cm to the left of lens 1, and the image formed on the screen has a magnification of +1.00. (a) Find the distance between the object and the screen. (b) Both lenses are now moved along their common axis while the object and the screen maintain fixed positions until the image formed on the screen has a magnification of +3.00. Find the displacement of each lens from its initial position in part (a). (c) Can the lenses be displaced in more than one way?
(a)

The distance between the object and the screen.
Answer to Problem 56CP
The distance between the object and the screen is
Explanation of Solution
Given info: The focal length of the left and right lenses are
Write the expression of thin lens equation for lens 1.
Here,
Substitute
Write the expression for magnification.
Substitute
Write the expression of magnification for a combination of two lenses.
Substitute
Write the expression to calculate the magnification for lens 2.
Substitute
Write the expression of thin lens equation for lens 2.
Here,
Substitute
Substitute
The distance between the object and the screen is,
Substitute
Thus, the distance between the object and the screen is
Conclusion:
Therefore, the distance between the object and the screen is
(b)

The displacement of each lens from its initial position.
Answer to Problem 56CP
The displacement of each lens from its initial position is
Explanation of Solution
Given info: The focal length of the left and right lenses are
Write the expression of thin lens equation for lens 1.
Here,
Substitute
Write the expression of magnification for lens 1.
Substitute
Write the expression of magnification for the combination of lenses.
Substitute
Write the expression to calculate the magnification of lens 2.
Substitute
Write the expression of lens equation for lens 2.
Substitute
Substitute
The distance between the object and the screen is,
Substitute
Solve the above quadratic equation to find the value of
When the value of
The displacement of object is,
Substitute
The displacement of the image is,
When the value of
The displacement of object is,
Substitute
The displacement of the image is,
Thus, the displacement of each lens from its initial position is
Conclusion:
Therefore, the displacement of each lens from its initial position is
(c)

Whether the lens can be displaced by more than one way.
Answer to Problem 56CP
It is possible to displace the lens in more than one way.
Explanation of Solution
Given info: The focal length of the left and right lenses are
Yes the lens can be displaced in more than one way.
The first lens can be displaced
Another way is, the first lens can be moved
Thus, it is possible to displace the lens in more than one way.
Conclusion:
Therefore, it is possible to displace the lens in more than one way.
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Chapter 35 Solutions
Physics for Scientists and Engineers with Modern Physics
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