An astronomer is trying to observe two distant stars. The stars are marginally resolved when she looks at them through a filter that passes green light with a wavelength near 550 nm. Which of the following actions would improve the resolution? Assume that the resolution is not limited by the atmosphere.

Required:
a. Changing the filter to a different wavelength? If so, should she use a shorter or a longer wavelength?
b. Using a telescope with an object lens of the same diameter but a different focal length? If so, should she select a shorter or a longer focal length?
c. Using a telescope with an objective lens of the same focal length but a different diameter? If so, should she select a larger or a smaller diameter?
d. Using an eyepiece with a different magnification? If so, should she select an eyepiece with more or less magnification?

To solve two distant stars we must use Rayleygh's criterion that establishes that two objects are separated if the central maximum of one coincides with the first minimum of the other, applying this to the expression for the diffraction of a slit

a sin θ = m λ

with m = 1

as the telescope has surgical objects, we must solve the problem in polar coordinates, leaving the expression

a sin θ = 1.22 λ

sin θ = 1.22 λ/a

now we can analyze the different statements

a) True. Diffraction decreases with decreasing wavelength

b) False. The focal length influences the magnification, the size of the image, but not the resolution of the same

c) True. As the diameter increases the diffraction decreases, we can observe closer stars

d) False. The focal length influences the magnification not the resolution,