When comparing apparent brightness on the magnitude scale, what factor of difference does one unit represent?
Answer
A factor of about 2.5 in brightness.
The apparent magnitude scale used for measuring stellar brightness is logarithmic, not linear, which is why small numerical differences equate to large visual differences. Specifically, a difference of one full magnitude between two stars represents a factor of approximately 2.5 in brightness when measured by light intensity. This relationship is exponential; for example, a star that is two magnitudes brighter (e.g., -0.5 vs +1.5) is $2.5 imes 2.5$, or $6.25$ times brighter.
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Sirius - the brightest star - YouTube
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