The magnitudes of two stars A and B are 2.5 a | vedclass

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(C) The relationship between the magnitudes $(m)$ and the brightness $(I)$ of two stars is given by the formula: $m_B - m_A = -2.5 \log_{10} \left( \f

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$10^3$

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(C) The relationship between the magnitudes $(m)$ and the brightness $(I)$ of two stars is given by the formula: $m_B - m_A = -2.5 \log_{10} \left( \frac{I_B}{I_A} \right)$.Given $m_A = 2.5$ and $m_B = -5$.Substituting these values into the formula: $-5 - 2.5 = -2.5 \log_{10} \left( \frac{I_B}{I_A} \right)$.$-7.5 = -2.5 \log_{10} \left( \frac{I_B}{I_A} \right)$.Dividing both sides by $-2.5$: $3 = \log_{10} \left( \frac{I_B}{I_A} \right)$.Therefore,the brightness ratio is $\frac{I_B}{I_A} = 10^3$.

The magnitudes of two stars $A$ and $B$ are $2.5$ and $-5$ respectively. The brightness ratio of $\frac{B}{A}$ is

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