There’s a dumb debate about a dumb photo going viral, again. This time, the hill we’ve decided to die on is number of sisters in this Instagram pic. How many sisters are there? Six sisters? Two sisters? (It’s two sisters.) But maybe four sisters?!!!
Instagram photographer Tiziana Vergari shot the image of girls sitting between two mirrors. The virtual images — the reflections of light that our eyes see as sisters — arise because when a photon hits a level, polished surface, it bounces off, rather than scattering or absorbing. The law of specular reflection states that a ray of light will reflect off a mirror at an equal angle from the normal (a hypothetical perpendicular line from the mirror). Put two mirrors in parallel, and any light traveling directly along the normal will move back and forth for theoretical infinity.
But you can’t actually create an infinite number of reflections, because in practice, mirrors aren’t perfectly reflective. Whenever a photon hits the reflective surface of a mirror, there’s a non-zero chance it will be absorbed. Even if you had a perfect dual-mirror getup, each reflected image doesn’t form simultaneously but at the speed of light. On a message board at Physics Forums, user boit writes out the scenario in which a guy leans on one mirror while facing another mirror a meter away:
His image (of his anterior aspect that is) will be formed after approximately 1/300,000,000 second. Image of his back will take a further 1/900,000,000 seconds more if he is one foot deep. Now in one second alone we have about 300,000,000 (300 million) images. After just half a minute you’ll have enough images to keep you occupied for over 70 years if you can manage to count four images a second. Nothing said of the images behind you. Well, that seems like infinity to us.
If we had two perfect mirrors and two immortal sisters and an immortal photographer, then, sure, we could have infinite reflections. But that’s not happening, no matter how swanky your Instagram filter is. So we can definitively say that there are a finite number of sisters, which at least narrows this thing down.
Also, there are clearly two girls in the photo.