# Diopter Focal Lengths and Powers

In photography, a "diopter" is a supplementary lens that is inserted between a camera lens and the subject to alter the focussing distance and magnification ratio. Depending on its application, it could range from a single symmetric element up to a complicated multi-element optically-corrected unit. The power of such a lens is a signed number having a magnitude equal to the inverse of the lens' effective focal length. When the focal length is in meters, the power has units of diopters. Positive and negative powers correspond, respectively, to converging and diverging lenses. For example, a "+4 diopter" is a converging lens with a focal length of 250 mm. The indicated lens power is usually that appropriate for use in air. What happens if the lens is immersed in some other medium, such as water?

f = (r/2)*n/[n(g) - n]

f(w) = (r/2)*n(w)/[n(g) - n(w)]

f(a) = (r/2)*n(a)/[n(g) - n(a)]

f(w)/f(a) = [n(g) - n(a)]/[n(g)*n(a)/n(w) - n(a)]

f(w)/f(a) = [n(g) - 1]/[0.75*n(g) - 1]

P(w)/P(a) = f(a)/f(w)

```n(g)    f(w)/f(a)  P(w)/P(a)
----------------------------
1.5       4.0        .25
1.6       3.0        .33
1.7       2.5        .40
1.8       2.3        .43
```