**Back to the Index of I2AO (Introduction to Astronomy Online)**

**A Bit of Maths **

*Intensity ratio and magnitude difference*

- The intensity ratio, I
_{A}/I_{B}, is equal to 2.512 raised to the power of the magnitude difference, m_{B}- m_{A}:

I

_{A}/I_{B}= 2.512^{(mB - mA)}

- By taking base 10 logs of both sides and rearranging, the formula may be solved for the magnitude difference:

m

_{A}- m_{B}= 2.5 log (I_{B}/I_{A})

- Sample results from this relationship are given in the following table.

- The distance modulus relates the distance (
*d*) to a star to the difference between its apparent magnitude (*m*) and its absolute magnitude (*M*). The V subscript refers to "V" band, or central wavelength for visible observations (as opposed to the blue or red end of the optical spectrum)._{V} *m-M*is called the distance modulus._{V}- The distance to a star (in parsecs) may be derived from the following equation.

d= 10^{(m - MV + 5)/5}

- Some sample distances derived from distance moduli are shown in the following table.

Author: Lesa Moore, 26th July 2017

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