A star at magnitude +3.5 is how many times fainter than a star at magnitude +1.0?

Answer

Roughly 15.8 times fainter.

To calculate the relative faintness when the magnitude difference is not a whole number, one must still utilize the base factor of 2.512, applying it to the fractional difference in magnitude. The difference between magnitude +1.0 and magnitude +3.5 is 2.5 magnitude steps. The calculation required is $(2.512)^{2.5}$. When this power calculation is performed, the resulting value is approximately 15.8. This means that the light reaching the eye from the star at magnitude +3.5 is roughly 15.8 times less intense than the light received from the star at magnitude +1.0, assuming both are observed under similar conditions. This confirms that even small numerical increases in magnitude correspond to substantial drops in observed brightness, reinforcing why the scale was originally inverted to prioritize the brightest phenomena.

A star at magnitude +3.5 is how many times fainter than a star at magnitude +1.0?

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