The amount of light entering the eye is controlled by the iris, which varies in diameter from 2 mm to 8 mm, according to field brightness. The resolving power of the eye is limited about equally by diffraction and the coarseness of the retinal structure to about 1 minute of arc. Because of this, the eye roams incessantly when examining an extended field.

It is no simple matter to relate the amount of light emitted by a star to how bright our perception of the star is. Under photopic (normal lighting) conditions, the human eye is most sensitive to light with a wavelength of 555 nm (5550 Angstroms), which is slightly greenward of yellow, and sensitivity drops off precipitously in both directions, so that sensitivity to pure red at 650 nm is barely more than one tenth as much. Our eyes register pure violet at 410 nm only .00012 times as well. At threshold (scotopic) levels of seeing, the spectral response function is shifted toward the longer wavelengths, peaking at slightly yellowish green (510 nm), though the drop-off follows an identical curve. This difference between photopic and scotopic vision is referred to as the Purkinjë effect, and occasionally results in conditions in which the green of trees appears to grow brighter just before night begins. This effect also helps explain why moonlight appears bluish.

Fortunately, since the blackbody curve of all stars follows a wide curve that takes in all visible wavelengths, the drop-off of longer and shorter wavelengths is not as strong an effect as it might be. In all the subsequent remarks, though, it should be noted that a yellow-white, sun-like star will appear brighter than a star whose visible emission peaks in the red or blue part of the spectrum.

The eye's contract sensitivity is nearly uniform over a great range of brightness levels, from about 1 to about 100,000 lumens/meter². This great range of adaptation of the eye must be associated with a change in the sensitivity of the retina, since the maximum variation in pupil size results in only a sixteen-fold change in retinal illumination. This change in adaptation level requires an appreciable amount of time, at least ten minutes after exposure to daylight, and as long as an hour after exposure to a very intense light source.

Representative values for various conditions:

Ordinarily stars fainter than the sixth magnitude are invisible to the naked eye, but, under optimal conditions, stars of magnitude 8.5 can just be perceived. The illumination produced by a star of magnitude m is represented by the formula

E_m=E1(1/2.5)^m-1

The illumination produced by a star of the first magnitude at zenith on a clear night is 8.3 x 10^-7 lumens/meter². By the formula above, it can then be computed that a star of magnitude 8.5 produces an illumination of about 8.3 x 10^-10 lumens/meter², or that of a candle at a distance of 21 miles if there were no atmospheric absorption. Compare this to the brightness of the non-galactic night sky, 5 x 10^-5 lumens/meter².

The sensitivity of any physical instrument can be expressed as the change in its indication produced by a given change in the quantity that it measures. In a voltmeter, for example, the sensitivity can be expressed as the change in scale readings produced by a given change in voltage. For the human eye, the response to light obeys a power law, not a logarithmic one as was once thought. As a result, perceived stellar brightness is proportional to the 0.4 power of actual brightness. Thus an actual brightness increase of one-hundredfold is only perceived as an increase of 6.3 times, and an increase of a thousandfold is only perceived as an increase of 15.8 times.

For example, Atlas, at mag -7.9, appears as bright as a 100wbulb at 212.4 meters, or a standard candle at a distance of 18.2 meters. A Galactic Core star at -14 would be as bright as a 100wbulb at 12.8 meters, or a standard candle at a distance of 1.1 meters.

This agrees with the figure given above (and elsewhere), that a star of magnitude 8.5 equals in brightness a candle at a distance of 21 miles (34.72 km.).