Radio waves from a star, of wavelength 230 m, reach a radio telescope by two sep

Question

Radio waves from a star, of wavelength 230 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 theta = 20.0 delta 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

from fig

sin20 = h / d2  

h = d2 sin20

d2 = h / sin20

and cos 40 = d1 / d2

and d2 - d1 = ( 230 / 2 ) = 115

we have h = d2 sin20 and d1 = d2 cos40

in the equation d2 - d1 = 115

substituting d1 = d2 cos40 we get

d2 - d2 cos40 = 115

d2 ( 1 - cos40 ) = 115

d2 = 491.546 m

d2 - d1 = 115 then d1 = 376.546 m

we have h = d2 sin20

h = 491.546 X sin20

h = 168.118 m

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