How far from source can light be seen if a 100W source radiates 600 nm light uniformly all directions and human eye can detect the light if 20 photons per sec enter dark eye with 7mm diameter pupil?

Answer 1

This is a complicated problem. But I can do it !

Energy of single photon energy = (h) (c) / (wavelength) = (6.626 x 10-34 J-s) (299,792,458 m/s) / (600 x 10-9 m)
= 3.3107 x 10-19 Joule
The eye requires 20 photons per sec = 6.6214 x 10-18 watt.

The ratio of the required power to the power of the source is the ratio of the area of a 7mm circle
to the area of the big sphere centered on the source.

(6.6214 x 10-18) / (100) = (pi x 0.00352) / (4 pi R2)

R2 = (100) (pi x 0.00352) / (4 pi x 6.6214 x 10-18)

R = (5 x 0.0035) / (sqrt(6.6214) x 10-9)

= 0.0068 x 109 = 6.8 x 106 meters

= 6,800 km (4,225.8 miles)

Wow !