As an admirer of Thomas Young, you perform a double-slit experiment in his honor

Question

As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.03 mm apart and position your screen 3.09 m from the slits. While Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 641 nm How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe? Express your answers in milimeters. First bright fringe: Number Second dark fringe: Number

Explanation / Answer

At the slits, constructive interference happens at multiples of full wavelengths (n?).
sin ? = n? / d

Now, at that angle, we look at the bright spots on the screen.
tan ? = x / L (x is the horizontal distance from the center of the screen, L is distance to screen)

For small angles, we can approximate that tan ? = sin ?.
n? / d = x / L
x = n ? L / d

First bright fringe, n = 1
x = (1) (641*10^-9 m) (3.09 m) / (1.03*10^-3 m) = 1.923 mm

For destructive interference (dark fringes), equation becomes:
x = (n - 0.5) ? L / d

Second dark fringe,
x = 1.5 (641*10^-9 m) (3.09 m) / (1.03*10^-3 m) = 2.8845*10^-3 m = 2.9 mm

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