# A Bit of Maths - Intensity Ratio and Distance Modulus

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A Bit of Maths

Intensity ratio and magnitude difference

• The intensity ratio, IA/IB, is equal to 2.512 raised to the power of the magnitude difference, mB - mA:

IA/IB = 2.512(mB - mA)

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

mA - mB = 2.5 log (IB/IA)

• Sample results from this relationship are given in the following table. Distance modulus and distance

• The distance modulus relates the distance (d) to a star to the difference between its apparent magnitude (m) and its absolute magnitude (MV). 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).
• m-MV is called the distance modulus.
• 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. 