5

I feel a little foolish asking this, but I keep reading sources which say that for an inverse square law relationship, e.g. light intensity vs distance from source, the intensity decays exponentially.

Are inverse square and exponential the same? I would think not, as I cannot find an algebraic way of writing $I \sim 1/r^2$ in the form of $I \sim \exp(ar)$. I do know exponential is the same as "geometric" increase (or decrease), as you keep multiplying by the same number every time.

This may be a symptom of the modern informal usage where people say something changing "exponentially" just means "a lot, very quickly" (don't get me started...). But I know the folks here can set me straight.

Nihar Karve
  • 8,672
RC_23
  • 12,766
  • 2
  • 17
  • 53

2 Answers2

14

Inverse square is not the same as exponential dropoff. Any source which says this is using "exponentially" in a colloquial way. Hopefully they don't then try to do mathematics immediately afterwards!

There are some exponential dropoffs in physics, such as the intensity of evanescent fields, but the drop off of normal light is decidedly an inverse square law and not an exponential law.

Cort Ammon
  • 53,814
  • 6
  • 103
  • 176
1

As far as I understand, in exponential equation the variable (x) is in the exponent. In a power function the variable is the base. In inverse square law, the intensity is inversely related to the square of the distance; the distance being the variable. Hence, inverse square law is a power function and not an exponential function.

Narayanan
  • 11