a) Two slits separated by a distance of d = 0.150 mm are located at a distance o

Question

a) Two slits separated by a distance of d = 0.150 mm are located at a distance of D = 630. mm from a screen. The screen is oriented parallel to the plane of the slits. The slits are illuminated by a coherent light source with a wavelength of lambda = 542E-6 mm. The interference pattern shows a peak at the center of the screen (m=0) and then alternating minima and maxima.
What is the pathlength difference between the two waves from the two slits at the first (m=1) maximum on the screen?

b) What is the pathlength difference between the two waves from the two slits at the first (m=0) minimum on the screen?
c) Calculate the distance on the screen between the central maximum (m=0) and the first (m=1) maximum (You can assume sin(theta) = tan(theta) = theta with  theta expressed in radians).

Explanation / Answer

Part A)

Path difference for maxima = m(wavelength) = (1)(542 X 10^-9)

Path Difference = 542 X 10^-9 m which is 542 X 10^-6 mm

Part B)
Path difference for minima = (m + .5)(wavelength)

Path Difference = (.5)(542 X 10^-9)

Path Difference = 271 X 10^-9 m which is 271 X 10^-6 mm

Part C)
Apply y/L = m(wavelength)/d

y/.63 = (1)(542 X 10^-9)/(1.5 X 10^-4)

y = 2.28 X 10^-3 m which is 2.28 mm

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