Calculate how magnification affects the surface brightness of deep-sky objects and find the optimal magnification range.
Enter your telescope aperture, telescope and eyepiece focal lengths, and the catalog surface brightness of the target in magnitudes per square arcsecond (about 22 for the outer regions of a faint galaxy).
Magnifying an extended object spreads its light over a larger apparent area. The dimming equals 5 × log10(magnification): at 100x, a 22 mag/arcsec² galaxy appears at 32 mag/arcsec² in the eyepiece.
For deep-sky objects the calculator also reports an empirical optimal magnification window of one-third to one-half of the aperture in millimeters — 67x to 100x for a 200mm scope — balancing image scale against dimming.
Magnification spreads an extended object's light over a larger apparent area. Surface brightness drops by 5 × log10(magnification) magnitudes per square arcsecond, so going from 50x to 100x costs about 1.5 magnitudes of brightness per unit area.
It expresses brightness per patch of sky: the magnitude a single square arcsecond of the object would have if it were a star. Higher numbers are fainter — a dark rural sky glows near 21–22 mag/arcsec², and many galaxy halos sit close to that.
This calculator uses the empirical range of one-third to one-half the aperture in millimeters. A 150mm telescope works best between 50x and 75x for most nebulae and galaxies: enough image scale to show structure without dimming the view excessively.
No — surface brightness in the eyepiece can never exceed the naked-eye view. A larger aperture lets you use more magnification while keeping the same exit pupil (aperture ÷ magnification), so the gain is image scale and total light rather than per-area brightness.