Suppose your telescope has perfect mirrors and is limited only by diffraction. If you are viewing with light of 400 nm wavelength, what diam

Question

Suppose your telescope has perfect mirrors and is limited only by diffraction. If you are viewing with light of 400 nm wavelength, what diameter mirror in a space telescope would have 1.0-km resolution of objects on Mars when viewed from above the earth at a time when the Earth-Mars distance of 80 million kilometers

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Orla Orla 5 years 2021-07-14T20:47:27+00:00 1 Answers 22 views 0

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  1. hongcuc2
    0
    2021-07-14T20:48:52+00:00
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    Answer:

    39 m

    Explanation:

    We are given that

    Wavelength=\lambda=400 nm=400\times 10^{-9} m

    1 nm=10^{-9} m

    y=1 km=1000 m

    1 km=1000 m

    Earth mars distance =x=80 million Km=80\times 10^9 m

    1million km=10^9 m

    sin\theta=\frac{1.22\lambda}{d}

    sin\theta=\frac{y}{x}

    \frac{y}{x}=\frac{1.22\lambda}{d}

    \frac{1000}{80\times 10^9}=\frac{1.22\times 400\times 10^{-9}}{d}

    d=\frac{1.22\times 400\times 10^{-9}\times 80\times 10^9}{1000}

    d=39.04 m\approx 39 m

    Diameter of mirror =39 m

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