Hey guys just 2 physics questions i need the solutions to and cant seem to figur

Question

Hey guys just 2 physics questions i need the solutions to and cant seem to figure out. 750 points, thanks in advance!

Astronomers have discovered a planetary system orbiting the star Upsilon Andromedae, which is at a distance 4.2 Times 1017 m from the earth. One planet is believed to be located at a distance of 1.9 Times 1011 m from the star. Using visible light with a vacuum wavelength of 550 nm, what is the minimum necessary aperture diameter that a telescope must have so that it can resolve the planet and the star? Times m Enter a number. In a setup like that in the figure below, a wavelength of 625 nm is used in a Young's double-slit experiment. The separation between the slits is d = 1.4 Times 10-5 m. The total width of the screen is 0.20 m. In one version of the setup, the separation between the double slit and the screen is LA = 0.28 m, whereas in another version it is LB = 0.46 m. On one side of the central bright fringe, how many bright fringes lie on the screen in the two versions of the setups? Do not include the central bright fringe in your counting. LA: Number of bright fringes = LB: Number of bright fringes =

Explanation / Answer

Angular resolution:

sinO = 1.22(lamda/d)

where O is the wavelength of the light
and d is the diameter of the lens

sinO = R/sqrt(R

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