Question

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)?

Answer 1

Answer:

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