algebra

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Solve problem.
Telephoto lens. find
the image distance i for an object that is 2,000,000 mm from
a 250-mm telephoto lens.

tel formula is 1/f=1/o + 1/i

1/250=1/2,000,000 + 1/i
5i(1/250)=(1/2,000,000 + 1/i)5i
1/50i = 5i/400,000i + 5i/5i
1/10i = 5i/80,000i + 5i/5i

I=8,000
Is this right?

• algebra -

1/250=1/2,000,000 + 1/i agree
I like powers of ten
10^-2 / 2.5 = 10^-6 / 2 +1/i

(2/2.5)10-2 = 10^-6 + 2/i

(2/2.5) 10^4 = 1 + 2*10^6 / i

8*10^3 = 1 + 2*10^6/i
8000 i = i + 2*10^6
7999 i = 2*10^6
i = 2,000,000/7999
i = 250 mm
In other words the object is effectively at infinity and its image is effectively at the focal point.

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