Question

3. Radio telescopes are often much larger in diameter than optical (i.e. visible light) telescopes; some of the larger ones have diameters of 100 meters, while the largest optical telescopes are only about 10 meters in diameter. Assume that radio telescopes observe at wavelengths around 1 cm, which is about 20,000 times longer than the wavelengths of visible light.

a) Explain why these large radio telescopes have much greater light-gathering power than large optical telescopes. Explain what quantities light-gathering power is related to, how much bigger or smaller these are in one case compared to the other.

b) Explain why these large radio telescopes actually have worse resolution than large visible-light telescopes. Be quantitative, and remember that smaller the value of the angular resolution (meaning the smaller the separation that can be resolved) the better the resolution.

Answer 1

3]

a] Light gathering power of a telescope is the ability of the telescope to collect more light. So, higher the size of the objective, greater will be the light gathering power of the telescope. Radio telescopes have very large apertures and objectives owing to the wavelength region in which it operates. Therefore, the light-gathering power for Radio telescopes will be very large.

The exact value by which the light-gathering power is higher for radio telescopes is:

P = Area_radio/Area_optical =

so, the light gathering power for radio telescope is 100 times greater than that of an optical telescope.

b]

Using Diffraction limit equation,

the angular resolution of an image will be:

where d is the diameter of the aperture.

for radio waves, the wavelength is 20000 times larger than optical wavelengths and so the resolution becomes very poor. It is for this reason that the diameter of the aperture has to be made very large to compensate for the large wavelength and give equivalent resolution as that of a visible range telescope.