Photons from 6th magnitude star

[Tom Mazanec]

How many visible light photons enter the eye each second from a star just barely bright enough to see?

[Hornblower]

How many visible light photons enter the eye each second from a star just barely bright enough to see?

I get a rough estimate of about 2,000 photons per second through fully dilated pupils. I worked from the following:

In visible range, photons average about 2 or 3 electron volts (eV) of energy.

One joule is about 0.6x 10^19 eV.

The Sun delivers about a kilowatt per square meter to Earth's surface, or 1,000 joules per second.

A 6th magnitude star is down about 33 magnitudes from the Sun, which is down a factor of about 10^13 in intensity.

A dilated pupil is roughly 25 square millimeters or 25x10^-6 square meter.

I crunched the numbers from there, mostly in my head, for an order of magnitude estimate. My number may be off a factor of 2 either way.

[StupendousMan]

A good number to remember is that a star of magnitude zero produces roughly 1 million photons per second per square centimeter of collecting area in the V-band (or R-band or I-band). Since a mag 6 star is about 250 times fainter than a mag 0 star, that means a mag 6 star produces about 4,000 photons per square centimeter per second in the V-band.

With Hornblower's estimate of the area of a dilated pupil, and allowing for the spectral sensitivity of the human eye, I'd say Hornblower's estimate is pretty good.