The approximate intensity ratio between two stars is 100. Thus the apparent visual magnitude difference between the stars is ______________.
A)1
B)5
C)10
D)100

Question

Quizplus · Accepted Answer

The intensity ratio is given by:
Intensity ratio = (brightness of star A) / (brightness of star B)
If the intensity ratio is 100, it means that star A is 100 times brighter than star B.
Using the formula for magnitude difference:
m2 - m1 = -2.5 log(I2/I1)
where m1 and m2 are the apparent visual magnitudes of the stars, and I1 and I2 are their intensities.
Assuming star A is brighter and has magnitude m1, we have:
I2/I1 = 1/100
-2.5 log(1/100) = -2.5 (-2) = 5
Therefore, the magnitude difference between the stars is 5.

The Approximate Intensity Ratio Between Two Stars Is 100