Chapter 38, Problem 38.74AP

Light of wavelength 632.8 nm illuminates a single slit, and a diffraction pattern is formed on a screen 1.00 m from the slit. (a) Using the data in the following table, plot relative intensity versus position. Choose an appropriate value for the slit width a and, on the same graph used for the experimental data, plot the theoretical expression for the relative intensity

$\frac{I}{{\mathrm{I}}_{max}^{}}=\frac{{\sin }^2\varphi }{{\varphi }^2}$

where ϕ = (πa sin θ)/λ. (b) What value of a gives the best fit of theory and experiment?

Position Relative to Maximum (mm)	Relative Intensity
0	1.00
0.8	0.95
1.6	0.80
3.2	0.39
4.8	0.079
6.5	0.003
8.1	0.036
9.7	0.043
11.3	0.013
12.9	0.000 3
14.5	0.012
16.1	0.015
17.7	0.004 4
19.3	0.000 3