Monochromatic light of wavelength is incident on a pair of slits separated by 2.

Question

Monochromatic light of wavelength is incident on a pair of slits separated by 2.45 10-4 m and forms an interference pattern on a screen placed 1.55 m from the slits. The first-order bright fringe is at a position ybright = 4.49 mm measured from the center of the central maximum. From this information, we wish to predict where the fringe for n = 50 would be located.

(a) Assuming the fringes are laid out linearly along the screen, find the position of the n = 50 fringe by multiplying the position of the n = 1 fringe by 50.0.

(b) Find the tangent of the angle the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum.

(c) Using the result of part (b) and dsinbright = m, calculate the wavelength of the light. nm

(d) Compute the angle for the 50th-order bright fringe from dsinbright = m. °

(e) Find the position of the 50th-order bright fringe on the screen from ybright = Ltanbright.

Explanation / Answer

Part A

position of 50th fringe

d = 50* 4.49

d = 224.5mm

Part B

tangent of first bright fringe

tan = 4.49*10^-3 / 1.55

tan = 2.89*10^-3

Part C

for small angle sin theta = tan = 2.89*10^-3

dsinbright = m

m = 1

2.45*10^-4 * 2.89*10^-3 =

= 709.7 nm

Part D

for 50th bright fringe

2.45*10^-4 sintheta = 50*

theta = 8.3 degree

Part E

Y = 1.55 tan(8.3)

Y = 0.226m

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