.

All angles in the parts a-c may be expressed by means of tables of inverse trigonometric functions of simple fractions, e.g. $\cos^{-1}(1/2)$, $sin^{-1}(2/7)$, etc.

Two vertical slits of width $a = 1200$ nanometers (nm) are separated (center to center) by a distance of $d = 3000$ nm and illuminated by light of wavelength $\lambda = 600$ nm. The light which passes through is then projected on a distant screen. Find:

a) The location (angles $\theta$) of all diffraction minima.

b) The location of all interference minima.

c) The location of all interference maxima.

d) Finally, draw a properly proportional figure of the resulting interference pattern between 0 and $\pi/2$ (on either side), indicating the maximum intensity in terms of the central maximum intensity that would result from a single slit.

e) For five points of extra credit, write down the algebraic expression for $I(\theta)$ in terms of $I_0$ (the central intensity of a single slit), defining all variables used (like $\phi$ and $\delta$) in terms of $a$, $d$, $\lambda$ and $\theta$.