The 2.4-m diameter Hubble space telescope has been placed into Earth orbit by the space shuttle.Assuming a wavelength of 710 nm,what angular resolution could this telescope achieve by Rayleigh's criterion? (1 nm = 10−⁹ m) A) 5.7 × 10−⁶ rad B) 7.5 × 10−⁶ rad C) 3.6 × 10−⁷ rad D) 2.5 × 10−⁷ rad

Question

Quizplus · Accepted Answer

Rayleigh's criterion states that the angular resolution is given by the ratio of the wavelength to the diameter of the telescope. Therefore, the angular resolution for the Hubble telescope is given by:
θ = 1.22 × λ/D
where λ = 710 nm and D = 2.4 m. Substituting these values, we get:
θ = 1.22 × 710 × 10^-9 / 2.4 = 3.6 × 10^-17 radians
Therefore, the angular resolution is 3.6 × 10^-17 radians, which is approximately equal to 3.6 × 10^-10 arcseconds. The closest answer choice is C, 3.6 × 10^-17 radians.

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