Understanding Magnitude
The magnitude system is a logarithmic scale that describes the brightness of celestial objects. A difference of 5 magnitudes corresponds to a factor of 100 in brightness.
The Formula
We can use the following formula:
```
m1 - m2 = 2.5 * log10(I2 / I1)
```
Where:
* m1 = Magnitude of the brighter star
* m2 = Magnitude of the fainter star
* I1 = Intensity of the brighter star
* I2 = Intensity of the fainter star
Calculation
1. Intensity Ratio: We know I1 / I2 = 40 (the brighter star is 40 times more intense).
2. Apply the Formula:
m1 - m2 = 2.5 * log10(1/40)
m1 - m2 = 2.5 * (-1.602)
m1 - m2 ≈ -4.01
Result
The difference in magnitudes between the two stars is approximately -4.01. This means the brighter star has a magnitude that is 4.01 units *smaller* than the fainter star. Remember, a smaller magnitude indicates a brighter object.
