Radio waves from a star, of wavelength 162 m, reach a radio telescope by two sep

Question

Radio waves from a star, of wavelength 162 m, reach a radio telescope by two separate paths, as shown in the figure below (not drawn to scale). One is a direct path to the receiver, which is situated on the edge of a cliff by the ocean. The second is by reflection off the water. The first minimum of destructive interference occurs when the star is = 30.0° above the horizon. Find the height of the cliff. (Assume no phase change on reflection. The image is not drawn to scale; assume that the height of the radio telescope is negligible compare to the height of the cliff.) m

Explanation / Answer

Given the incident ray makes an angle of 30 deg with the ocean surface, so from "angle of incidence equals angle of reflection" the reflected ray also makes angle 30deg with ocean.
The first interference minimum will occur when the distance from the reflection point to the receiver is a half wavelength (= 81 m).

The signal reflected off the water travels further.

For the destructive interference, the signals need to be 50% out of phase, which occurs when the sloping distance

is half a wavelength = 162/2=81 m

The vertical component is sin30 = vert/162

vert height = sin30/81 m = 6.17*10^-3m

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