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