Question

A telescope of aperture diameter $5m$ is used to observe the moon from the earth. Distance between the moon and earth is $4\times {10}^{5}km$. The minimum distance between two points on the moon’s surface which can be resolved using this telescope is close to (Wavelength of light is $5500\stackrel{\circ }{A}$)

• A. $60m$
• B. $20m$
• C. $600m$
• D. $200m$

Answer 1

The correct option is A

$60m$

Step 1. Given Data:

Diameter of the aperture, $D=5m$

Distance between the moon and the earth, $d=4\times {10}^{8}m$

Wavelength, $\lambda =5500\times {10}^{-10}m$

Let the minimum distance between two points on the moon’s surface be $s$.

Step 2. Minimum angle, $\theta$ for clear resolution:

$$\begin{gathered} \theta =1.22\left(\frac{\lambda }{D}\right)\dots \left(1\right) \\ s=d\theta \\ \theta =\frac{s}{d}\dots \left(2\right) \end{gathered}$$

Step 3: Calculating the minimum distance between two points, $s$

Equating equation $\left(1\right)$ and equation $\left(2\right)$,

$$\begin{gathered} \frac{s}{d}=1.22\left(\frac{\lambda }{D}\right) \\ \frac{s}{4\times {10}^8}=\frac{1.22\times 5500\times {10}^{-10}}{5} \\ s=53.68m \end{gathered}$$

Nearest option is $60m$

Hence, the correct option is (A).