A2 - Module 5 - Resolving Powers

Hello, would be REALLY grateful if anyone could help me on this!!

''The dish of a radio telescope has holes of diameter 20mm spaced close together in its reflecting surface in order to reduce the weight of the dish. Explain why the performance of this telescope will be far more satisfactory when receiving signals of frequency 7.5 x 10^8 Hz than when receiving signals of frequency 1.5 x 10^10 Hz.''

I calculated the wavelength of each of these frequencies:

d = 20 x 10^03 m
When f = 7.5 x 10^8, wavelength = 0.4m
When f = 1.5 x 10^10, wavelength = 0.02m.

The dish sounds like it looks like wire mesh, in which case for the signal to be received, the size of each hole of the mesh needs to be 1/20 of the wavelength. In which case:

For f= 7.5 x 10^8, wavelength = 0.4m, so 0.4/20 = 0.02m
For f = 1.5 x 10^10, wavelength = 0.02m, so 0.02/20 = 0.001m.

Doesn't this mean that the signal received from waves of a frequency of 1.5 x 10^10 Hz will be more satisfactory? Which is exactly what we're trying to prove isn't true i.e. that the other wave is better?

:frown:

Please help!!!! xxx

Reply 1

F1 fanatic

16

Jess89

Hello, would be REALLY grateful if anyone could help me on this!!

''The dish of a radio telescope has holes of diameter 20mm spaced close together in its reflecting surface in order to reduce the weight of the dish. Explain why the performance of this telescope will be far more satisfactory when receiving signals of frequency 7.5 x 10^8 Hz than when receiving signals of frequency 1.5 x 10^10 Hz.''

I calculated the wavelength of each of these frequencies:

d = 20 x 10^03 m
When f = 7.5 x 10^8, wavelength = 0.4m
When f = 1.5 x 10^10, wavelength = 0.02m.

The dish sounds like it looks like wire mesh, in which case for the signal to be received, the size of each hole of the mesh needs to be 1/20 of the wavelength. In which case:

For f= 7.5 x 10^8, wavelength = 0.4m, so 0.4/20 = 0.02m
For f = 1.5 x 10^10, wavelength = 0.02m, so 0.02/20 = 0.001m.

Doesn't this mean that the signal received from waves of a frequency of 1.5 x 10^10 Hz will be more satisfactory? Which is exactly what we're trying to prove isn't true i.e. that the other wave is better?

:frown:

Please help!!!! xxx

You want a wavelength much much longer than the holes, so that it "sees" a filled in dish and is unaffected by the holes. A wavelength of order the whole would obviously be diffracted, and mess the signal up with interference effects. A wavelength that was much shorter would pass right through and would be lost (ie undetected).

Reply 2

anonpls123

OP

Thanks Stu!! :biggrin:

x

A2 - Module 5 - Resolving Powers

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