Question

(a) What is the angular separation of two stars if their images are barely resolved by a refracting telescope with a lens diameter of 94 cm and a focal length of 14 m. Assume ? = 550 nm. (b) Find the distance between these barely resolved stars if each of them is 8.7 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern in meters, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens "errors."

Answer 1

a)

D = diameter = 94 cm = 0.94 m

= wavelength = 550 nm = 550 x 10^-9 m

angular separation is given as

= 1.22 /D

= 1.22 (550 x 10^-9)/(0.94) = 7.14 x 10^-7 rad

b)

r = distance = 8.7 light yr = 8.7 x 9.46 x 10¹⁵ m

d = distance

Using the equation

d = r

d = (8.7 x 9.46 x 10¹⁵ ) (7.14 x 10^-7)

d = 5.88 x 10¹⁰ m