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Apparent magnitude
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===Magnitude addition=== Sometimes one might wish to add brightness. For example, [[Photometry (astronomy)|photometry]] on closely separated [[double star]]s may only be able to produce a measurement of their combined light output. To find the combined magnitude of that double star knowing only the magnitudes of the individual components, this can be done by adding the brightness (in linear units) corresponding to each magnitude.<ref>{{cite web | title=Magnitude Arithmetic|url=http://www.caglow.com/info/wtopic/mag-arith | work=Weekly Topic | publisher=Caglow | access-date=30 January 2012 | archive-url=https://web.archive.org/web/20120201203951/http://www.caglow.com/info/wtopic/mag-arith | archive-date=1 February 2012|url-status=live}}</ref> <math display="block"> 10^{-m_f \times 0.4} = 10^{-m_1 \times 0.4} + 10^{-m_2 \times 0.4}. </math> Solving for <math>m_f</math> yields <math display="block"> m_f = -2.5\log_{10} \left(10^{-m_1 \times 0.4} + 10^{-m_2 \times 0.4} \right), </math> where {{mvar|m<sub>f</sub>}} is the resulting magnitude after adding the brightnesses referred to by {{math|''m''<sub>1</sub>}} and {{math|''m''<sub>2</sub>}}.
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