An antenna for receiving television signals from a satellite has a diameter of 3 m.The signals have a wavelength of 24 cm.If the diameter of the antenna is reduced to 50 cm,for what signal wavelengths does the antenna still have the same angular resolution?
A)4.0 cm
B)6.0 cm
C)8.0 cm
D)1.4 m
E)24 cm

Question

Quizplus · Accepted Answer

For an antenna to have the same angular resolution, the ratio of its diameter (D) to the wavelength (λ) should be constant. This is commonly referred to as the Rayleigh criterion. 
So, we can write:
D1/λ1 = D2/λ2
Where D1 = 3 m, λ1 = 24 cm = 0.24 m, and D2 = 0.5 m (reduced diameter).
We can solve for the wavelength that satisfies the above equation:
λ2 = (D2/D1)λ1 = (0.5/3) x 0.24 = 0.04 m = 4.0 cm
Therefore, the antenna will have the same angular resolution for signals with a wavelength of 4.0 cm. 
The other wavelengths given in the answer choices are either too small or too large, and therefore, the antenna will not have the same angular resolution for those wavelengths.

An Antenna for Receiving Television Signals from a Satellite Has