Question

Calculate the separation of two points on moon that can be resolved using $600\text{cm}$ telescope. Given distance of moon from earth, $=3.8\times {10}^{10}\text{cm}$. The wavelength most sensitive to eye is $5.5\times {10}^{-5}\text{cm}$.

• A. $4100\text{cm}$
• B. $4200\text{cm}$
• C. $4180\text{cm}$
• D. $4280\text{cm}$

Answer 1

The correct option is C $4180\text{cm}$

Given:
$b=600\text{cm}\lambda =5.5\times {10}^{-5}\text{cm}$

Distance between moon and earth, $D=3.8{\times }^{10}\text{cm}$

Limit the resolution of a telescope,

$\Delta \theta =\frac{1.22\lambda }{b}=\frac{1.22\times 5.5\times {10}^{-5}}{600}=1.1\times {10}^{-7}\text{rad}$

If $x$ is the separation of two points on the moon, that can be resolved.


$\Rightarrow \Delta \theta =\frac{x}{D}$

$\Rightarrow 1.1\times {10}^{--7}=\frac{x}{(3.8\times {10}^{20})}$

$\Rightarrow x=1.1\times {10}^{-7}\times 3.8\times {10}^{10}$

$\Rightarrow x=4180\text{cm}$

Hence, $\left(A\right)$ is the correct answer.