Question

You measure distances from the center of a diffraction pattern (y) to a series of dark fringes on a screen that is 0.3000 ± 0.0005 m away from the 0.04-mm wide slit you are using to create the pattern. You create a plot of y (in m) vs m and get a slope for the best-fit line of 0.005525 ± 8.175 10-6. What is the wavelength of the laser you used to collect the data?

Answer 1

To solve this problem it is necessary to apply the concepts related to Slit Diffraction.

The expression for separation between fringes is given by,

$d= \frac{\lambda D} {a}$

Where,

$\lambda =$ Wavelength

d = Separation between fringes

a = Slit width

D = Distance between the slits

Re-arrange to find $\lambda$, we have that

$\lambda = \frac{da}{D}$

Replacing with our values we have

$\lambda = \frac{(0.005575)(4*10^-5)}{0.3}$

$\lambda = 743.15*10^{-9}$

$\lambda = 743.14nm$

Therefore  the wavelength of the laser you used to collect the data is 743.14nm