The resolving power of the human eye is 1'. A | vedclass

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(A) The angular resolution $	heta$ is given by $	heta = \frac{d}{r}$,where $d$ is the separation between objects and $r$ is the distance from the ey

Vedclass · Accepted Answer

$10$

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(A) The angular resolution $	heta$ is given by $	heta = \frac{d}{r}$,where $d$ is the separation between objects and $r$ is the distance from the eye.Given $	heta = 1' = \left( \frac{1}{60} ight)^\circ = \left( \frac{1}{60} ight) 	imes \frac{\pi}{180} \, 	ext{rad}$.Given $d = 3 \, m$.Substituting the values into the formula:$\frac{1}{60} 	imes \frac{\pi}{180} = \frac{3}{r}$$r = 3 	imes 60 	imes \frac{180}{\pi}$Using $\pi \approx 3.14159$:$r = \frac{32400}{3.14159} \approx 10313 \, m \approx 10.3 \, km$.Rounding to the nearest given option,the correct answer is $10 \, km$.

The resolving power of the human eye is $1'$. At what distance $r$ (in $km$) can two objects separated by a distance of $d = 3 \, m$ be seen as distinct?

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