# A star has an apparent magnitude of 10 and an absolute magnitude of -5. How far away is it?

##### 1 Answer

The star is

#### Explanation:

We know that the apparent magnitude

And the absolute magnitude

Difference between apparent and absolute magnitudes of an object,

Magnitude system is based on the response of the human eye which shows a logarithmic response. Also the magnitude system, a logarithmic scale, assumes that a factor of

Therefore, we have this scale of base

For two stars

Taking the log of both sides and using

This is commonly expressed in the form

We know that intensity of a light source follows inverse square law of distances. After comparing intensities and magnitudes of two different stars as in equation (1) let us compare the intensities and magnitudes of the same star at two different distances.

Substituting

When

Above can be rewritten as

Inserting given values in (2) above we get