Solution 2.3.2.
It can be shown that the intensity distribution function for grating diffraction is given as,
I  I0
sin 2 x sin 2 N
.

x2
sin 2 
Where, x 
a sin 
 (a  b) sin 
and  


Here, a  width of each slit, b  distance of opaque space,  is the angle of diffraction. The
separation between any two slits is ‘ a  b' . ' a  b' is called the grating element or grating constant.
Sometime gratings are specified by rulings per cm d =
A code for an example is given:
Clear all;
theta_angle = -180:0.005:180;
theta = theta_angle*/565.71;
lambda = 532e-9;
a = 1e-6;
b = 10e-6;
d = a+b;
N=1000;
x = (pi*a*sin(theta))/lamda;
beta = (pi*d*sin(theta))/lamda;
I = (sin(x)./x.*sin(N*beta)./beta).^2;
plot (theta_angle, I);
xlabel (‘Angle’);
ylabel (‘Grating Diffraction Pattern’);
1
.
ab