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A star A is 100 times brighter than star $B$. Then, $m_{B}-m_{A}$ the difference in their apparent magnitudes is
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Verified Answer
The correct answer is:
5
Given, $\frac{I_{A}}{I_{B}}=100$
Using magnitude equation,
$$
\begin{aligned}
m_{B}-m_{A} &=-2.5 \log \left(\frac{I_{B}}{I_{A}}\right) \\
&=-2.5 \log \left(\frac{1}{100}\right)=-2.5 \times-2=5
\end{aligned}
$$
Using magnitude equation,
$$
\begin{aligned}
m_{B}-m_{A} &=-2.5 \log \left(\frac{I_{B}}{I_{A}}\right) \\
&=-2.5 \log \left(\frac{1}{100}\right)=-2.5 \times-2=5
\end{aligned}
$$
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