Question

4. An adult human eye has a diameter of 8 mm. (a) What is the theoretical smallest possible angle (diffraction limit) that can be discerned at 550 nm? [arcsec] (b) Compare this with the average angular diameter of Jupiter as seen from Earth [arcsec]. Assume Jupiter is at a distance of 5 AU and it has a diameter of 138,350 km.

Answer 1

The minimum angle ( diffraction limit) is given as

= 1.22 / D

where is wavelength, D is aperture diameter

= 1.22 * 550e-9 / 8e-3

= 8.387e-5 rad

we need this in arcsec

1 rad = 206265 arcsec

so,

= 17.3 arcsec

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Now, find angular diameter of jupiter

' = 206265 ( d / D)

where d is diameter and D is distance

convert 5 AU to meters

5 AU = 7.48e+11 m

' = 38 arcseconds ( approx)

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