Question

To resolve two distant stars that are separated by 0.5 arcseconds using a telescope observing at a wavelength of 500 nanometers, what is the minimum required diameter of the telescope aperture in meters?

Accepted Answer

To determine the minimum diameter of a telescope aperture required to resolve two points, we use the Rayleigh criterion formula, which states that the angular resolution in radians is equal to 1.22 multiplied by the wavelength of light, divided by the diameter of the aperture. First, convert the angular separation from arcseconds to radians. There are 3600 arcseconds in one degree and 180 degrees in pi radians, so one arcsecond is approximately 4.848 times 10 to the negative 6 radians. Therefore, 0.5 arcseconds equals 2.424 times 10 to the negative 6 radians. Next, convert the wavelength of 500 nanometers into meters, which is 5 times 10 to the negative 7 meters. Rearranging the Rayleigh criterion formula to solve for the diameter gives the diameter as equal to 1.22 times the wavelength divided by the angular resolution. Plugging in the values, you multiply 1.22 by 5 times 10 to the negative 7 meters and divide the result by 2.424 times 10 to the negative 6 radians. This calculation yields a minimum required diameter of approximately 0.2516 meters.

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To resolve two distant stars that are separated by 0.5 arcseconds using a telescope observing at a wavelength of 500 nanometers, what is the minimum required diameter of the telescope aperture in meters?