Suppose a reflecting telescope in an orbiting satellite has a mirror of diameter

Question

Suppose a reflecting telescope in an orbiting satellite has a mirror of diameter 2.27 m.

a) Find the minimum angular separation that is resolvable with this telescope if you are using:
i. Visible light of frequency 4.07x1014 Hz: radians
ii. Ultraviolet light of frequency 5.2x1016: radians

b) Suppose this telescope is looking at the moon, distance 3.84x108 m away. How far apart must objects be if they are resolved by this telescope:
i. Under visible light (f = 4.07x1014 Hz): m
ii. Under ultraviolet light (f = 5.2x1016 Hz): m

Explanation / Answer

rayleight criterion

a)

i)

sin theta = 1.22 lambda/D

theta = arcsin(1.22* (3E8/4.07E14)/2.27))=3.96E-7

ii) theta = arcsin(1.22* (3E8/5.2E16)/2.27))=3.1E-9

b) i) d = L tan theta = 3.84E8*tan(3.96E-7)=152.064 m

ii) d= 3.84E8*tan(3.1E-9)=1.19 m

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