Evil Dr Ganymede wrote:So how bright does an object in the sky have to be before it can blind you if you look at it for longer than a few seconds?
It's the
surface brightness, rather than the visual magnitude, that makes the difference. The Sun is an extended light source with a surface brightness of 1.9e9 candela/m^2. If you get farther away from it, it'll appear smaller in the sky, and therefore will shed less light, and so will have a higher visual magnitude (higher=dimmer); but angular area for area, its surface brightness will be the same, so it'll still burn a hole in your retina (just a smaller hole). This'll go on until you get so far away the solar disc falls below the diffraction limit of your eyes (about one minute of arc), at which point its apparent disc stops getting smaller ... its light is
always smeared over a minute of arc, so its surface brightness on your retina starts to fall as you move even farther out. Pluto's distance is around the point where that protective effect is just beginning to occur, as julesstoop points out.
The corollary is that if a star has a surface brightness considerably less than the Sun's, it won't burn your retina even though you approach it closely enough for it to have the same visual magnitude as the Sun seen from Earth ... it'll be a dimmer source spread over a bigger angular area.
The threshold value for a retinal burn is somewhere between 10^7 cd/m^2 (incandescent lamp filament) and 10^8 cd/m^2 (carbon arc light). So stars with a black-body temperature >3500K (M3V up) will scar your retina; <3000K (M7V down) won't.
Evil Dr Ganymede wrote:I mean, what's the apparent magnitude of a 75W bulb in a living room, if you're standing in that room? Anyone got a handy way to grok this sort of thing?
An apparent visual magnitude of zero corresponds to an illumination of 2.54e-6 lux (with some variation depending on the star temperature). Since you can read by a 75W bulb, and the threshold for comfortable reading is about 100 lx, then your bulb is 100/2.54e-6 = 4e7 times brighter than magnitude zero.
The equivalent magnitude difference is 2.5*log(4e7) = 19, so your bulb has an apparent magnitude of about -19.
Grant