Schwarzschild exponent

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Karl Schwarzschild developed a formula that is used to determine the intensity of the blackening of a photographic emulsion . This formula contains an exponent, which is called the Schwarzschild exponent after him .

${\displaystyle i=f(I\cdot t^{p})}$

where:
i: blackening of the photo plate
f: blackening curve (see gradation and saturation )
I: intensity of starlight
t: exposure time
p: Schwarzschild exponent, for real films always p <1 (mostly just under 0.9)

So that a weak galaxy can be displayed twice as large in astrophotography (with the same telescope opening and the same blackening of the photo plate ), the exposure time must not only be quadrupled, but approximately fivefold.

The formula does not fit the mechanism of the Schwarzschild effect and therefore only applies to small variations and is only of historical significance.