How many time brighter than a star with an apparent magnitude....?

Question

of 11.5 is a star with an apparent magnitude of 1.5?

Answer 1

The scale of magnitude is geometric. It is calibrated in such a way that a difference of 5 on the magnitude scale means a brightness ratio of 100.

6.6 is 100 times brighter than 11.5
1.5 is 100 times brighter than 6.5

Therefore
1.5 is 100*100 times brighter than 11.5
(10,000 times).

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The ratio between each successive magnitude level is the fifth root of 100 (approx. 2.512 times). Also written 100^(1/5) "one hundred to the power one fifth".

Therefore the ratio between your two stars (magnitude 11.5 and magnitude 1.5; a difference of 10 magnitude levels) is:
[ 100^(1/5)]^10 = 100^(10/5) = 100^2 = 10,000

or

2.5118864...^10 = 10,000

Answer 2

The decrease the plain magnitude fee, the brighter it sounds as though on earth. 0.a million is under 0.4, so Rigel seems brighter than Procyon. it is the full portion of "obvious magnitude".

Answer 3

(2.5)^(11.5-1.5) times brighter.