Young\'s double-slit experiment underlies the instrument landing system used to

Question

Young's double-slit experiment underlies the instrument landing system used to guide aircraft to safe landings at some airports when the visibility is poor. Although real systems are more complicated than the example described here, they operate on the same principles. A pilot is trying to align her plane with a runway as suggested in the figure below. Two radio antennas (the black dots in the figure) are positioned adjacent to the runway, separated by d = 38.0 m. The antennas broadcast unmodulated coherent radio waves at 28.0 MHz. The red lines in the figure below represent paths along which maxima in the interference pattern of the radio waves exist. The pilot "locks onto" the strong signal radiated along an interference maximum and steers the plane to keep the received signal strong. If she has found the central maximum, the plane will have precisely the correct heading to land when it reaches the runway as exhibited by plane A. Suppose the plane is flying along the first side maximum instead as is the case for plane B. How far to the side of the runway centerline will the plane be when it is 2.06 km from the antennas, measured along its direction of travel? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, m It is possible to tell the pilot that she is on the wrong maximum by sending out two signals from each antenna and equipping the aircraft with a two-channel receiver. The ratio of the two frequencies must not be the ratio of small integers (such as -). Explain how this two-frequency system would work and why it would 4 not necessarily work if the frequencies were related by an integer ratio.

Explanation / Answer

Ans :- a] = c/f = 3*10^8 / 28*10^6 = 10.7m

B] the first side maximum is at angle given by

dsin = (1)

d= 38; sin = 0.28

y = L*sin = 2060*0.28 =580.05m

c] The intent is to inform the pilot about the signal that corresponds to the central maximum. The signal with = 10.7 m would show maxima at 0, 16.3°, 34.3°, 57.6°. A signal of wavelength, say, 11.23 m would show maxima at 0, 16.3°, 34.2°, 57.3°. the only value in common is 0. A strong signal for both frequencies would indicate that the airplane was traveling along the central maximum; thus, straight on the runway. If 1 and 2 were related by a ratio of small integers in 1/2 = n1/n2, then the equations d sin = n2 1 and d sin = n1 2 would both be satisfied for the same nonzero angle. Thus the pilot could approach on an inappropriate bearing, and run off the runway immediately after touchdown.

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