Radio waves from a star, of wavelength 338 m, reach a radio telescope by two sep

Question

Radio waves from a star, of wavelength 338 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 ? = 26.0° 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

let height of cliff be H

and x be the length of ray from reflected ground to telescope

by geometry

path difference = x - xcos(2 * 26 )

xcos(90-26) = h

xsin(26) = h

phase difference = (x - xcos(2 * 26 )) *2pi/(338) = pi

x = 439.716523716

h = 439.716523716 sin(26) =   192.759036763 m

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