Question

The diameter of moon is $3.5\times 10^{3}km$ and its distance from the earth is $3.8\times 10^{5}km$. The focal length of the objective and eyepiece are $4m$ and $10cm$ respectively. The limit of resolution of diameter of the image of the moon will be approximately

• A. $2^{\circ }$
• B. $21^{\circ }$
• C. $40^{\circ }$
• D. $50^{\circ }$

Answer 1

Answer: (B)

Here, $\alpha =\frac{3.5\times 10^3}{3.8\times 10^5}$,rad
$=\frac{3.5}{3.8\times 100}\times \frac{180^{\circ }}{\pi }$
$=\frac{3.5\times 180\times 7^{\circ }}{38\times 100\times 22}$
Also, $M=\frac{f_o}{f_e}=\frac{400}{10}=40$
$\therefore$ Limit of resolution, $\beta =\frac{40\times 35\times 180\times 7^{\circ }}{35\times 100\times 22}$
$=21.1^{\circ }\approx 21^{\circ }$