Question 176868
Given the formula for a lens:
:
{{{1/f = 1/o + 1/i}}}
:
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:
:
{{{1/250 = 1/2000000 + 1/i}}}
:
Let's get rid of the denominator 2000000 by multiplying both sides (all terms) of this equation
by 2000000 and the equation then becomes:
:
{{{2000000/250 = 1 + 2000000/i}}}
:
Do the division on the left side by dividing 250 into 2000000 and the equation becomes:
:
{{{8000 = 1 + 2000000/i}}}
:
Get rid of the 1 on the right side by subtracting 1 from both sides and this reduces the
equation to:
:
{{{7999 = 2000000/i}}}
:
Get rid of the denominator i on the right side by multiplying both sides of the equation (all terms)
by i to get:
:
{{{7999i = 2000000}}}
:
Solve for i by dividing both sides of the equation by 7999 and you have:
:
{{{i = 2000000/7999}}}
:
Do the division on the right side (use a calculator) and you find that the image distance is
:
{{{i = 250.0312539}}}
:
So the answer is that the image distance from the lens is about 250.03 mm.