Question

The objective of a telescope A has diameter 3 times that of the objective of telescope B, How much greater amount of light is gathered by A as compared to B?

• A. $\frac{1}{9}$
• B. $\frac{1}{3}$
• C. 3
• D. 9

Answer 1

The correct option is D 9

$\begin{array}{c}\text{Let light gathered by}A,B\text{be}{L}_A,L_B\\ \text{Given}{d}_A=3d_B\\ \text{Since}d=2r\\ r_A=3{\gamma }_B\end{array}$

$\begin{array}{c}\text{We know that}\\ \text{Light gathered}\propto \text{Area.}\end{array}$

$\begin{array}{cc}\Rightarrow \frac{LA}{LB}& =\frac{t{r}_A^2}{\pi r_B^2}(\because r_A=3r_B)\\ & =9:1\end{array}$