SOLUTION: Telephoto lens. Use the formula (1/f=1/o+1/i) to find the image distance i for an object that is 2,000,000 mm from a 250 mm telephoto lens.

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Question 176868: Telephoto lens. Use the formula (1/f=1/o+1/i) to find the image distance i for an object that is 2,000,000 mm from a 250 mm telephoto lens.
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
Given the formula for a lens:
:

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In which f is the focal length of the lens, o is the object distance from the lens, and
i is the image distance from the lens.
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For this problem, you are told that f, the focal length of the lens, if 250 mm and that o
the object distance from the lens is 2,000,000 mm. (The object is 2,000 meters away, which
is a long distance compared to the focal length of the lens.)
:
All units in this equation will be mm. Substitute the two values you are given (one for f
and one for o) and you have:
:

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Let's get rid of the denominator 2000000 by multiplying both sides (all terms) of this equation
by 2000000 and the equation then becomes:
:

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Do the division on the left side by dividing 250 into 2000000 and the equation becomes:
:

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Get rid of the 1 on the right side by subtracting 1 from both sides and this reduces the
equation to:
:

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Get rid of the denominator i on the right side by multiplying both sides of the equation (all terms)
by i to get:
:

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Solve for i by dividing both sides of the equation by 7999 and you have:
:

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Do the division on the right side (use a calculator) and you find that the image distance is
:

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So the answer is that the image distance from the lens is about 250.03 mm.