Blog #4: WS2.1, #2

2. You are floating in space with Sandra Bullock. It's dark and there is a barely discernible 1W lightbulb ahead of you. You know the eye must receive ~10 photons in order to send a signal to the brain that says, "Yep, I see that." How far away is it?

L = $10^7$ erg/s (luminosity)
a = $\pi 0.25^2 cm^2 = 0.196cm^2$ (area of your pupil)
$\lambda$ = 500*$10^{-7}$cm (wavelength in the visible light portion of the spectrum)
$t_{refresh}$ = 0.1s (time it takes for your eyes to absorb the photons)
R = ? cm

$E_{photon} = \frac{hc}{\lambda}$
$F = \frac{10E_{photon}}{at_{ref}} = \frac{L}{A}$
$\frac{10hc}{at_{ref}\lambda} = \frac{L}{4\pi R^2}$
$R = (\frac{Lat_{ref}\lambda}{40\pi hc})^{1/2}$

$R = (\frac{(10^7 erg/s)(0.196cm^2)(0.1s)(500*10^{-7}cm}{(40\pi )(6.6*10^{-27} erg*s)(3*10^{10} cm/s)})^{1/2}$
R = 2.0*$10^7$cm