2. Double Slit: You have a double slit with slit width 0.040 mm and slit separation 0.150 mm.
(a) How many interference fringes would appear in the central diffraction envelope?
(b) Suppose I double the separation, what happens to (i) the location of the first diffraction minimum, (ii) the number of interference fringes in the central maximum?
(c) Suppose I keep the same separation but now make the slit width half of its previous value, what happens to (i) the location of the first diffraction minimum, (ii) the number of interference fringes in the central maximum?
3. Diffraction Grating: I shine light onto a diffraction grating with 550 lines/mm.
(a) What are the angles for all orders of diffraction maxima for blue light of wavelength 450 nm?
(b) What are the angles for all orders of diffraction maxima for red light of wavelength 650 nm?
(c) When the beam of light hits the grating, it has a diameter of 2.4 mm. What is the resolving power in first order?
(d) For visible light, what is the minimum separation of wavelengths that can be resolved?
4. Resolution: You want to visually observe a binary star system, Sirius, that is located 8.6 light-years away. Treat the two stars as point sources separated by 15 astronomical units (1 a.u. = distance from earth to sun). What diameter telescope would you need to resolve this system as two stars in visible light? Repeat for a similar binary system located 430 light-years away.
Two sources of phase difference:
(a) Optical Path Length difference between rays, where
optical path length = (index of refraction) (physical path length)
(b) Phase introduced upon reflection: If light is in a material of higher index, and reflects from a boundary with a material of lower index, phase change of 0 , "Hi off lo change of zero", and conversely, "Lo off hi, change of pi" and we can focus on the phase angle or call it a change of 1/2 wavelength.
5. Soap Bubble: Consider a thin layer of soap bubble held in the circular wand (fig 36-14, p. 878) with air on both sides. Find the thicknesses of the soap bubble (assume the water/soap solution has an index n1 = 1.33) for which there is (a) constructive interference (b) destructive interference of reflected light of wavelength lambda.
(c) Find the type of interference you expect when the film becomes very thin. What is the thickness of the film in Figure 36-14 where the first visible reflected light is seen?
In all cases assume the light is incident perpendicular to the film.
6. Anti-Reflection Coating: Suppose I put a thin layer, thickness L, of MgF2, n = 1.38, onto glass, n = 1.5. Light of wavelength lambda, 500 nm, is shone onto the system perpendicular to the film. Find the conditions which lead to (a) constructive and (b) destructive interference. (c) What is the minimum thickness of the material that will cause destructive interference?
7. Dielectric Mirror: Onto glass, n = 1.5, I put layers of ZnS (n = 2.30, L = 54.3 nm) and MgF2 (n = 1.38, L = 90.6 nm) as shown. Four reflections are shown. Find the type of interference (Const., Dest.) between rays 1 and 2, 2 and 3, and 3 and 4 when light of wavelength 500 nm is shone onto the system. In all cases assume the light is incident perpendicular to the film.
8. Michaelson Interferometer [diagram in text Fig. 36-17, p. 881]: Suppose the vertical path, d2, has a pipe around it which can be evacuated. Also I make the starting condition d1 = d2. Initially both paths are filled with air, and I have a bright fringe. As I slowly evacuate the pipe to produce a vacuum (n = 1), I count 774 bright fringes appearing and disappearing in the telescope. Find the index of refraction of air.