Derive the intensity distribution of the double slit pattern, Eq$.36\mathrm{.}9$ of your text, using an

approach similar to what we used in class to derive the intensity of a single slit diffraction pattern.

Specifically:

a$)$ Start by writing down the magnitudes of the electric fields coming from each slit at a point P on

the screen. Explicitly include the phase difference due to the path difference.

b$)$ Write down the total electric field.

c$)$ Using that the intensity of the light is proportional to the square of the electric field, show that

the measured intensity $($the time$-$averaged value$)$ agrees with Eq$.36\mathrm{.}9.$