Question

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

MATLAB CODE:

theta=(pi/180)*[-20:0.1:20];
s_theta=sin(theta);
alpha1=pi*sin(theta);
i_ratio1=((sin(alpha1))./alpha1).^(2);
alpha2=5*pi*sin(theta);
i_ratio2=((sin(alpha2))./alpha2).^(2);
alpha3=10*pi*sin(theta);
i_ratio3=((sin(alpha3))./alpha3).^(2);
plot(theta, i_ratio1, theta, i_ratio2, theta, i_ratio3)

PLOT:

a: lambda a: 5lambda a- 10lambda 0.9 0.8 0.7 0.6 0.5 0.3 0.2 0.1H 0.3 0.2 0.1 0.1 0.2 0.3 04 theta (radianst