Coherent Laser

Measuring maxima and minima on screen due to coherent laser light (wavelength = 700 nm) incident on two slits?

Please refer to the following diagram: http://i5.photobucket.com/albums/y163/pharrellsaydontdoitthesame/post1.jpg

A person is measuring maxima and minima on a screen due to coherent laser light (wavelength = 700 nm) incident upon two narrow slits. The two slits are separated by a distance, d. The screen is 2.0 m away from the two slits. The person is supposed to measure the distance along the screen from a given maxima to the central maximum. The person mistakenly measures the distance along the screen, y, from the m = +3 maxima on one side on the central maximum to the m = -2 minima on the other side of the central maximum (as shown in the diagram). In the diagram, dark spots correspond to minima, and white spots correspond to maxima. What is the value of "d" if the person measures y to be 0.008 m?

The distance from the central maximum to the n = 3 maximum is

x1 = 3*(λ/d)*L

The distance from the central maximum to the n = -2 mimumum is

x2 = 1.5*(λ/d)*L

x1 + x2 = 3*(λ/d)*L + 1.5*(λ/d)*L = 4.5*(λ/d)*L

0.008 = 4.5*(λ/d)*L

d = 4.5*(λ/.008)*L = 4.5*700*10^-9*2.0/.008 = 7.9*10^-4 m = 0.79 mm

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