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25 August, 13:13

Which telescope has a better (smaller) angular resolution: a 2-m telescope observing visible light (wavelength 5.0*10-7 m) or a 10-m radio telescope observing radio waves (wavelength 2.1*10-2 m) ?

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  1. 25 August, 13:18
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    the most accurate telescope

    Explanation:

    The resolution limit of any telescope is determined by the diffraction effects, which is described by the equation

    a sinθ = m λ

    Where a is the width of a linear slit, λ the wavelength and m e an integer that indicates the order of diffraction, in this case m = 1 is used to have the width of the central maximum,

    sin θ = λ / a

    Since the angles are very small, we can approximate the sine to the value of the Angle

    θ = λ / a

    In the case of circular objects, polar coordinates must be used, the expression changes to a constant

    θ = 1.22 λ / a

    Let's apply this equation to the two telescopes

    Telescope

    θ₁ = 1.22 5.0 10⁻⁷ / 2

    θ₁ = 3.05 10⁻⁷ rad

    Radio Telescope

    θ₂ = 1.22 2.1 10⁻² / 10

    θ₂ = 2.56 10⁻³ rad

    We compare the two values

    θ₁ <θ₂

    the most accurate telescope
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