Radio waves from a star, of wavelength 188 m, reach a radio telescope by two sep
ID: 1481232 • Letter: R
Question
Radio waves from a star, of wavelength 188 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.) m
Explanation / Answer
The direct ray is at angle to the horizontal.
The ray that hits the water surface is parallel to the direct ray.
Hence the angle of this ray to the horizontal water surface is also .
By law of reflection, the reflected ray also is at angle to the water surface.
The path difference between these rays is the distance between the point on the water surface and the receiver.
Which we shall denote as L
sin = h /L
Since there is destructive interference and as we have not considered the phase change due to reflection, L = / 2 .
h = sin / 2. = 94 sin 22° = 35.21 m
Hence height of the cliff is 35.21 m.
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