Example 3

The diagram shows the distance

between an object and a lens and the distance

between the lens and the image it creates of the object.

and

represent the focal points of the two-sided lens. (Note that these points are symmetric about the lens at line

.) Use the diagram and the function

to find

and

if the focal length

of the lens is

and

Define the variables in the function.
Substitute the defined variables into the given function and simplify.
Graph the simplified equation.
Describe the domain of the function and what that implies for the number of possible solutions for and .
Solve to find the value(s) of as described in step 4.
Find and interpret the solutions in terms of the locations of the object and image in relation to the lens.

This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit www.walch.com for more information.

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