What is the meaning of this (potentially humorous) mathematical equation?

Question

The equation in the image shown below (outlined in blue) was found on the cover of a magazine, along with several other "math equation jokes" like the "I heart pi" joke. My friends and I haven't been able to figure this one out, and I can't seem to identify the last part of the equation.

It's obvious that the first part (square root of negative one) is "I", and the heart symbol is self-explanatory. I suspect that "$mc^2$" corresponds to "e" (but perhaps this is intended to be purely phonetic, or maybe intended to mean "energy").

Answer 1

• $\sqrt{-1}$ is referring to $i$, the imaginary unit. $i$ satisfies the equation $i^2 = -1$. This is sometimes written as $i = \sqrt{-1}$, though this is abuse of notation in some cases depending on your definition of $\sqrt{}$.
• ♥ is a heart shape, which is often interpreted as meaning or somehow being related to love.
• $E = mc^2$ is Einstein's formula for the rest mass-energy of a massive body. $m$ is the rest mass (or invariant mass), and $c$ is the speed of light.
• $\frac1f=\frac1i+\frac1o$ is the thin lens equation, which describes the distances of an object and the image of that object (which may be real or virutal) relative to a thin refractive lens in geometric optics. $f$ is the focal length of the lens which is defined by this formula in the limit $o \rightarrow \infty$.

So, this line could be read as (ignoring capitalization, punctuation, etc.) "I love eo". As the OP states, this image is taken from Edmund Optics, which I guess abbreviates their name as "eo". With that interpretation, it seems to be a promotional piece of some sort. This image on their website confirms that this is the intended interpretation.

Answer 2

Those number 1's are sloppy -- or is the bracketed amount on the right actually $-2$ instead of $-1$. I will assume $-1$.

Then, the item in brackets can be rewritten as $$ \frac{if}{f-i} $$

But, I am not sure what this means. Following from before, "I love [E]nergy if "over" f-i???