1) Use Excel or Maple to actually add together the cosines or exponentials to describe the 3-slit interference pattern and thus compute the following.

a) The actual intensity distribution as a function of angle, θ.

b) The ratio of the intensity of the main bumps to the intensity of the little bumps.

c) The width (at half maximum intensity) of the main bumps compared to the width of the bumps in the two-slit interference pattern.

2) Red laser light, wavelength 632nm passes through a single slit 0.04mm wide and falls on a screen 1m away. Plot the intensity distribution seen on the screen assuming that the maximum intensity anywhere in the pattern is 1.

3) A mixture of red light, 632nm, green light, 500nm, and blue light, 430nm, falls onto a single slit 0.025mm in width. Assuming that the light is bright enough for you to see it clearly, describe what you will see on a screen 1m away.

4) 5) When both diffraction and interference are taken into account in the double slit experiment, discuss the effect of increasing a) The wavelength,

b) The slit separation,

c) The slit width.

5) In a double-slit experiment, the slit separation, d, is 2.0 times the slit width, w. How many bright interference fringes are in the central diffraction envelope?

6) People who work with high power optical lasers are at risk from light reflected from lenses in their optical setups. Explain how a thin coating of Magnesium Oxide (MgO), refractive index n = 1.4, can be used to completely eliminate reflection from a glass lens when it is placed in the beam of a λ = 700nm ruby laser. What must be the thickness of the layer?

7) Short wavelength radio waves, with wavelengths in the cm region, are called microwaves. They can be effectively transported as simple plane waves by confining them in rectangular metal tubes called waveguides. One curious device that is used in such systems is called a directional coupler. It consists of two separate waveguides connected by two small holes placed ^λ∕₄ apart. By considering interference and relative phases of the two waves explain why the device, shown below, transmits power from entrance I out to both exits II and IV but NOT to exit III. What happens if, instead, you shine energy into aperture II?

8) By considering the ideas of diffraction, explain why AM radio waves (frequencies from 0.5-2MHz) are received better in mountains that FM radio waves (frequencies 88-108MHz).

9) Sketch the 2-D diffraction pattern that you would expect to see when a large diameter laser beam (λ = 632nm) is shone through a rectangular slit 30μm high and 10μm wide onto a screen 1m away.

10) Hold a CD, music side up, in your hand and look at the reflection of a distant light source in the disc. Describe and explain what you see. Try this for several different kinds of light source such as an incandescent bulb, a flourescent bulb, and a sodium street light.