SOLUTION: I have this last story problem to do and am confused, can someone help? Use the formula 1 over f = 1 over o + 1 over i to find the image distance i for an object that is 2,000,0

Question 130030: I have this last story problem to do and am confused, can someone help?
Use the formula 1 over f = 1 over o + 1 over i to find the image distance i for an object that is 2,000,000 mm from a 250-mm telephoto lens.
So confused, can someone help? Thanks
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given the formula for a lens:
.

.
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.
.
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:
.

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

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

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

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

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

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

.
So the answer is that the image distance from the lens is about 250.03 mm.
.
If you are into physics and science, what does this tell you? It says that as long as the
object is far away from the lens, the image will always be about 250 mm from the lens. Therefore,
the image will be pretty much in focus if the film or the digital sensors plates for digital
cameras are located about 250 mm behind the lens. This would be a pretty good sized camera
since 250 meters behind the lens is nearly 10 inches, so the camera would be around
10 inches deep.
Maybe this will make sense to you. It does to serious photographers.
.
Hope this helps you to learn a little about math and also some about the physical
characteristics of lenses.
.
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