Concept explainers
The Lens Equation If F is the focal length of a convex lens and an object is placed at a distance x from the lens, then its image will be at a distance y from the lens, where F, x, and y are related by the lens equation
Suppose that a lens has a focal length of 4.8 cm and that the image of an object is 4 cm closer to the lens than the object itself. How far from the lens is the object?
The distance of the object from the lens.
Answer to Problem 114E
The distance of the object from the lens is
Explanation of Solution
Given:
The equation that relates F, x and y is
Formula used:
Quadratic formula:
The solution of a quadratic equation of the form
Calculation:
The focal length of convex lens is
Since the image of an object is 4 cm closer to the lens than the object itself, it can be written that
Substitute
Simplify the above equation as follows.
Compare this equation with the general form
Here
Use the quadratic formula to obtain the roots of the given equation.
Simplify further as follows.
Substitute
Substitute
Note that, the distance cannot be negative.
Thus, the distance of the object from the lens is
Chapter 1 Solutions
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