Two stars situated at distances of 1 and 10 l | vedclass

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(C) The apparent brightness $I$ of a star is given by the formula $I = \frac{L}{r^2}$,where $L$ is the real brightness (luminosity) and $r$ is the dis

Vedclass · Accepted Answer

$1:100$

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(C) The apparent brightness $I$ of a star is given by the formula $I = \frac{L}{r^2}$,where $L$ is the real brightness (luminosity) and $r$ is the distance from the observer.Since both stars appear to have the same brightness,we have $I_1 = I_2$.Therefore,$\frac{L_1}{r_1^2} = \frac{L_2}{r_2^2}$.Given $r_1 = 1$ light year and $r_2 = 10$ light years.Substituting these values,we get $\frac{L_1}{L_2} = \frac{r_1^2}{r_2^2} = \left( \frac{1}{10} \right)^2 = \frac{1}{100}$.Thus,the ratio of their real brightness is $1:100$.

Two stars situated at distances of $1$ and $10$ light years respectively from the earth appear to possess the same brightness. The ratio of their real brightness is

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