Question

Star A on apparent magnitude of 7, and its light intensity is 100 times dimmer than that of star B, what is the apparent visual magnitude of star B?

Answer 1

From the problem statement we know

$m_A=7$

$I_B=100I_A$

Then from Pogson's formula

$\frac{I_B}{I_A}=2.512^{m_A-m_B}$

write down

$\frac{100I_A}{I_A}=2.512^{7-m_B}$

$100=2.512^{7-m_B}$

$\lg{(100)}=\lg{(2.512^{7-m_B})}$

$2=0.4(7-m_B)$

$5=7-m_B$

$m_B=7-5$

$m_B=2$