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1. 1. The problem statement, all variables and given/known data

A radiotelescope is positioned at a height of h=150m on a cliff overlooking the sea. A very distant galaxy emitting radiowaves, wavelength 3m, is at an angle above the horizion. The radiowaves reach the telescope both directly and after reflection off the water surface. Show that if =57degrees, then the 2 rays interfere destructively, so that the signal received is zero. Note that the refractive index,n,of the sea is greater than that of air

2. Relevant equations
dsin=(m+1/2) for destructive interference.

3. The attempt at a solution
Tried substituting the values into the equation, with d=2hsin, and expected to get m as an integer, but didnt..
2. Maybe this diagram will help

a) there is a phase change of 180 degrees on reflection
b) for destructive interference the path difference of the ray reaching the telescope T via BPRT compared with AT must be such that it is out of phase by 180 degrees.
c) the path difference is the distance PRT
d) find the length RT on the triangle ORT, and then PR in the triangle PRT. They are both right angle and you know one side and one angle.

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Updated: February 15, 2010
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