The <magnitude zero point> is defined by the reference response $I_0$. With zero magnitude assigned to that reference, the <apparent magnitude> is
$$
\boxed{m=-2.5\log_{10}\left(\frac I{I_0}\right).}
$$
The two responses must use the same <photometric passband> and instrumental weighting. If the reference has assigned magnitude $m_0$ instead, add $m_0$ to the right-hand side.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 338 / 1 / c / i / Solution

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A photometric system specifies <photometric passbands> and <magnitude zero points>, allowing calibrated brightness comparisons.

Photometric system

A magnitude zero point fixes the reference measurement $I_0$ in a specified <photometric passband>. Relative to a zero-magnitude reference, the <apparent magnitude> is $m=-2.5\log_{10}(I/I_0)$. Both measurements must use the same passband and calibration convention.

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