Question

Which equation shows the distance $d$, given its brightness $b$ and luminosity $L$?

$b=\frac{L}{4\pi d^2}$

• A. $d=\frac{1}{2}\sqrt{\frac{L}{\pi b}}$
• B. $d=\sqrt{\frac{L}{2\pi b}}$
• C. $d=\frac{\sqrt{L}}{2\pi b}$
• D. $d=\frac{L}{2\sqrt{\pi b}}$

Answer 1

Answer: (A)

$d=\frac{1}{2}\sqrt{\frac{L}{\pi b}}$

Given, $b=\frac{L}{4\pi d^2}$

where $b$ is the brightness and $L$ is the luminosity

$\Rightarrow d^2=\frac{L}{4\pi b}$

$\therefore d=\sqrt{\frac{L}{4\pi b}}$

$\therefore d=\frac{1}{2}\sqrt{\frac{L}{\pi b}}$