Two radio antennas separated by d = 292 m as shown in the figure below simultane

Question

Two radio antennas separated by d = 292 m as shown in the figure below simultaneously broadcast identical signals at the same wavelength. A car travels due north along a straight line at position x = 1 370 m from the center point between the antennas, and its radio receives the signals. Note: Do not use the small-angle approximation in this problem. (a) If the car is at the position of the second maximum after that at point O when it has traveled a distance y = 400 m northward, what is the wavelength of the signals? _____ m b) How much farther must the car travel from this position to encounter the next minimum in reception? _____ m In the figure below (not to scale), let L = 1.20 m and d = 0.170 mm and assume the slit system is illuminated with monochromatic 490-nm light. (a) Calculate the phase difference between the two wave fronts arriving at P when theta = 0, 500 degree. _____ rad (b) Calculate the phase difference between the two wave front arriving at P when y = 5.00 mm. _____rad (c) What is the value of theta for which the phase difference is 0.333 rad? _____ degree (d) What is the value of theta for which the path difference is lambda/4? _____ degree

Explanation / Answer

A) By double slit formula,

lambda = d sin theta /m

lambda = (292/2)*sin (arctan (400/1370))

= 40.92 m

B) 40.92= (292/2.5)*sin (arctan (y/1370))

arcsin(40.92*2.5/292) =arctan (y/1370)

0.358 = arctan (y/1370)

y = 1370*tan 0.358

Required distance = y - 400

= 512-400

= 112 m answer

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