The astronomical magnitude scale.
The scale below is given as an instructive tool, to give a general idea of how the magnitude scale works. The scale below is intended to be roughly visual; the human eye's (dark-adapted) detection efficiency peaks around 495 nanometers, while the formal photoelectric V peak (a filtered band intended to be close to visual) is around 550 nm; CCDs tend to peak around 700 nm. The examples are given for integer values are not "exact", in that celestial objects are often measured to a precision or 0.1 or 0.01 magnitude; for example, Sirius shines at V = -1.47 (Yale Bright Star Catalogue), and the planet Venus varies in brightness generally from magnitude -4.5 to -3.7. Note that a comet of magnitude 5 will not be as easy to see as a star of magnitude 5, because that same amount of brightness that is concentrated in a point for the star is spread out over a region of the sky for a diffuse comet with a relatively-large coma.
Magnitude Needed to see an object of this brightness*
Examples
-26m : the sun
-13m : full moon
-6m : crescent moon
-4m : naked eye: easy even from large cities planet Venus
-2m : naked eye planet Jupiter
-1m : naked eye brightest star, Sirius; totally-eclipsed moon; C/1995 O1 (Hale-Bopp) near peak
0 m : naked eye: difficult if near bright summer evening star artificial lights but generally Vega; C/1996 B2 visible even from large cities (Hyakutake) at peak
+1m : naked eye: brilliant as seen from planet Saturn dark, rural areas
+2m : naked eye: difficult but visible from stars of Big Dipper small cities and suburbs; diffuse Halley's comet in objects such as comets may require 1986 near peak small binoculars from urban areas
+3m : naked eye: rural, suburban, small city faintest naked-eye binoculars: bright, urban areas stars visible fromνmany smaller cities/inner suburbs;
+4m : naked eye: (outer) suburbs faintest naked-eye binoculars: cities (stars), suburban stars visible from areas (diffuse objects such as comets) many smaller cities/(outer) suburbs
+5m : generally binocular objects from urban moons of Jupiter and suburban areas; faintest naked-eye stars visible from "dark" rural areas located some 40 miles (60 km) from major cities

+6m : binocular objects from suburban areas; planet Uranus faintest naked-eye stars visible from"dark" rural areas located some 100 miles (150 km) from major cities
+7m : binoculars; faintest naked-eye stars brightest minor visible from "dark" rural areas planet (asteroid) located some 140 miles (200 km) from and about 1-2 major cities and some 30 miles (50 km) comets each year from nearest town of population 5000 or so
+8m : binocular objects; from urban areas, such planet Neptune objects may only be visible with small telescopes
+10m : from dark sky, objects visible with at any given 20x80 binoculars; from brighter sites, time, there are a larger telescope is needed usually a couple of comets this bright
+11m : general limiting visual brightness# of comets with a 15-cm-aperture reflector
+12m : general limiting visual brightness# of at any given time, comets with a 20-cm-aperture reflector there are usually a half dozen comets this bright
+13m : general limiting visual brightness# of comets with a 25-cm-aperture reflector
+14m : general limiting visual brightness# of Pluto at its brightest stars with a 20-cm-aperture reflector
+15m : general limiting visual brightness# of comets with a 50-cm-aperture reflector
+19m : general limiting photographic brightness#of comets with a 50-cm-aperture
reflector
+21m : general limiting brightness of stars with a 60-cm-aperture reflector + CCD
+22m : general limiting brightness# of comets with a CCD and 150-cm-aperture reflector
* naked-eye viewing assumes 20-20 vision (corrected or uncorrected)
# from a dark, rural site; "visual" as compared to "photographic" or
"CCD-detected"; "reflector" means "reflecting telescope"