Two point sources of light of wavelength 600 nm are being viewed by a telescope with aperture width 2.0 cm. What is the smallest angular separation at which the two sources can be resolved? A) 7.3 × 10^-5 rad B) 3.7 × 10^-5 rad C) 7.3 × 10^-5 deg D) 3.7 × 10^-5 deg E) 4.2 × 10^-3 deg

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Quizplus · Accepted Answer

The smallest angular separation can be found using Rayleigh's criterion, which states that the two sources can only be resolved if the peak of one source falls on the first minimum of the other. This occurs when the angular separation between the sources is equal to the wavelength divided by the aperture width. Thus, the smallest angular separation is given by (600 nm)/(2.0 cm) = 3.0 × 10^-4 rad. However, this is only the resolution limit for an infinitely large telescope. In practice, the resolution will be worse due to factors such as atmospheric turbulence and imperfections in the optics. The actual resolution of a telescope is often measured using the full width half maximum (FWHM) of the point spread function, which is a measure of the angular size of the blurred image of a point source.

Two Point Sources of Light of Wavelength 600 Nm Are