Problem 2:

Problem 3:

Problem 4:

Determine the Fourier series components of the periodic function shown below.  You may do this analytically or numerically.

Problem 5:

Assume light shines on a series of equally spaced slits.  The spacing between the slits is d.  Show that the intensity distribution of the interference pattern of the N equally-spaced sources is given by

I=I₀sin²(N(kd/2)sinq)/sin²((kd/2)sinq)

Use our derivation of the diffraction pattern of a single slit and the figure below to derive the equation.  Assume that instead of a continuous distribution of source points you have N equally spaced source points.

Calculate the Fourier transform of the triangular function shown below.  You may do this analytically or numerically.

Problem 7:

Convolute the two functions shown below.  You may do this analytically, graphically, or numerically.