Radio waves from a star, of wavelength 288 m, reach a radio telescope by two sep
ID: 1304903 • Letter: R
Question
Radio waves from a star, of wavelength 288 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 ? = 22.0 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.)
Explanation / Answer
Given the incident ray makes an angle of 23 deg with the ocean surface, so from "angle of incidence equals angle of reflection" the reflected ray also makes angle 23 deg with ocean.
The first interference minimum will occur when the distance from the reflection point to the receiver is a half wavelength (= 144 m). This distance is the hypotenuse of a right triangle with the cliff height being the "opposite" side. So;
cliff height = (144)Sin(22)
= 53.94 m
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