In comparing first magnitude Deneb with second magnitude Polaris, we find that:
A)Polaris is in reality much more luminous.
B)Deneb must be much hotter than Polaris.
C)Deneb appears 2.5 times brighter to us than does Polaris.
D)Polaris is really 100 times brighter than nearby Deneb.
E)Deneb is really much closer than Polaris.

Question

Quizplus · Accepted Answer

Magnitude is a measure of brightness as seen from Earth, and the scale is logarithmic. A difference of one magnitude corresponds to a brightness ratio of roughly 2.5. Therefore, a first magnitude star like Deneb appears 2.5 times brighter to us than a second magnitude star like Polaris. However, the actual brightness or luminosity of a star depends on both its distance and its intrinsic properties like temperature and size, so we cannot determine that from magnitude alone. Magnitude is a measure of brightness as seen from Earth. The lower the magnitude, the brighter the object. A difference of one magnitude represents a difference in brightness of 2.5 times. Therefore, since Deneb has a magnitude of 1.25 and Polaris has a magnitude of 2, the difference in their brightness is 2.5^(2-1.25) = 2.5^0.75 = 1.78. Therefore, Deneb appears 1.78 times brighter than Polaris to us. This means that choice C is correct. Choices A, B, D, and E are not supported by the information given.

In Comparing First Magnitude Deneb with Second Magnitude Polaris, We