Question

Radio waves from a star, of wavelength 266 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 G 24 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.) Direct Radio path telescope Reflected path

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Answer #1

δ=λ2-λ1=δ2(1-sinα)

If the first minimun(δ=λ/2)
occur when θ= 24°then
α =180-(θ+90+θ)=42°

δ2 = 1/(1-sinα)
= [(266/2)]/1-sin42°=133/0.330
=403 m
h=δ2sin24°= 163 m

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