Question

1. Two narrow slits are illuminated by a laser with a wavelength of 543 nm. The interference pattern on a screen located x = 4.50 m away shows that the third-order bright fringe is located y = 7.20 cm away from the central bright fringe. Calculate the distance between the two slits. ("1st order" means m=1, "second order" means m=2, etc).

Answer 1

Use the formula

d*sin(q) = m*l where d = distance between slits, q = angle made by the mth fringe, m = 0, +/- 1, +/-2 ... and l = wavelength

Now you can approximate sin(q) for q << 1 by sin(q) ~ q

In the problem you are told the screen is distance L = 4.5m away and the second fringe is at y 0.091 m so you can estiamte q by

q ~ y/L = 0.091/4.7 = 0.01936 radians and then sin(q) = 0.01936 so now you can solve for d

d = m*l/sin(q) = 2* 543x10^-9m/0.01936 = 5.93x10^-6 m = 5.61 um