The 2.4-m diameter Hubble space telescope has been placed into Earth orbit by the space shuttle.Assuming a wavelength of 684 nm,what angular resolution could this telescope achieve by Rayleigh's criterion? (1 nm = 10−⁹ m) A) 3.5 × 10−⁶ rad B) 4.3 × 10−⁶ rad C) 2.8 × 10−⁶ rad D) 3.4 × 10−⁷ rad E) 2.4 × 10−⁶ rad

Question

Quizplus · Accepted Answer

By Rayleigh's criterion, the angular resolution 𝜃 is given by 𝜃=1.22𝜆/D, where 𝜆 is the wavelength of light and D is the diameter of the telescope. Substituting the given values, we get 𝜃=1.22×684×10^-9/2.4=3.44×10^-7 rad. Rounding off to two significant figures, we get 𝜃=3.4×10^-7 rad, which corresponds to option D.

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