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I and f are positive for lenses (and negative for mirrors) if they are on the opposite side of the lens or mirror from the light from the object:
converging lens | diverging lens |
I > 0 | I < 0 |
R_{enter} > 0 | R_{enter} < 0 |
R_{exit} < 0 | R_{exit} > 0 |
f > 0 | f < 0 |
M < 0 | M > 0 |
real image | virtual image |
This is called the thin lens equation.Combining it with the definition of magnification, we find that
M = f / (f - O)This means that for negative f (diverging lenses and convex mirrors), 0 < M < 1.
It also means that for positive f (converging lenses and concave mirrors),
This is called the lens maker's equation.If f in measured in meters, s = 1/f is the lens strength measured in diopters.
For compound lenses, the strengths are additive.
n_{2} / I + n_{1} / O = (n_{2} - n_{1}) / R.
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©2011, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.