Question

MATLAB

When monochromatic light passes through a narrow slit it produces on a screen a diffraction pattern consisting of bright and dark fringes. The intensity of the bright fringes, I, as a function of $\Theta$ can be calculated by:

$I = I_{max}(\frac{sin\alpha }{\alpha })^{2}$

where

$\alpha = \frac{\pi a}{\lambda }sin\Theta$

Where $\lambda$ is the light wave length and a is the width of the slit. Plot the relative intenstiy I / I_max as a function of $\Theta$ for -20^o <= $\Theta$ <= 20^o. Make one plot that contains three graphs for the cases

a = 10$\lambda$, a = 5$\lambda$, and a = $\lambda$. Label the axes, and display a legend.

Answer 1

I = I _max (Sin alpha/alpha)^2 where alpha = pi a/lambda Sin theta Code: theta = (p I/180) * (- 20: 0 . 1: 20): s - theta = Sin (theta): alpha 1 = pi * sin (theta): I - ratio 1 = ((Sin (alpha 1)) , (alpha 1)^(2): alpha 2 = 5 * pi * Sin (theta): I - ratio 2 = ((sin (alpha 2)) (alpha 2)^(2): alpha 3 = 10 * pi * sm (theta): I - ratio 3 = ((Sin (alpha 3)) \ alpha 3):^(2): plot (theta, I - ratio: theta,