You are outside watching a distant white light in the sky on a dark, clear night

Question

You are outside watching a distant white light in the sky on a dark, clear night thinking that this might be an alien spaceship finally coming to take you away. But then at some poin you notice that it is not a single light, but rather two lights that are approaching you, and you realize that it is just another jet approaching the regional airport. About how far away was the jet when you were able to recognize that it was indeed a jet and not an alien spacecraft if the two lights on the opposit wings of the jet are 19.4 m apart and your pupil diameter is 0.6 m.

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Explanation / Answer

There are many situations in which diffraction limits the resolution. The acuity of our vision is limited because light passes through the pupil, the circular aperture of our eye. Be aware that the diffraction-like spreading of light is due to the limited diameter of a light beam, not the interaction with an aperture. Thus light passing through a lens with a diameter D shows this effect and spreads, blurring the image, just as light passing through an aperture of diameter D does.

In this question

The distance (s= 19.4 m) between two objects(jet lights) at a distance r away and separated by an angle ? is s=r?.

where ? is the limit of resolution given as ? = 1.22 k/D

K = wavelength of light = generally 650 nm in jet lights

D = diameter of aperture = 0.006 m in this case

so r = s/? = s*D/1.22 k

= (19.4 *0.006)/(1.22* 650 *10 ^(-9))

   =0.0001467842 * 10 ^(-9) m

= 146784.3 m

= 146.784 Km

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