Question

The 305 mdiameter Arecibo radio telescope detects radio waves with wavelengths from 3 to 100 cm. What is the angle in radians between two just-resolvable 5.00 cm wavelength point sources for this telescope?

Answer 1

θ = 2.00x10⁻⁴ rad

Step-by-step explanation:

To find the angle we need to use the Rayleigh equation:

`\theta = 1.22(\lambda)/(D)`

Where:

θ: is the angular resolution =?

λ: is the wavelength = 5.00 cm

D: is the diameter of the aperture = 305 m

Hence, the angle is:

`\theta = 1.22(\lambda)/(D) = 1.22(5.00 \cdot 10^(-2) m)/(305 m) = 2.00 \cdot 10^(-4) rad`

Therefore, the angle between two just-resolvable wavelength point sources is 2.00x10⁻⁴ radians.

I hope it helps you!