Section 1
Interference
Violet light falls on two slits separated by $1.90 \times 10^{-5} \mathrm{m} .$ A first-order bright band appears$13.2 \mathrm{mm}$ from the central bright band on a screen $0.600 \mathrm{m}$ from the slits. What is $\lambda ?$
Yellow-orange light from a sodium lamp of wavelength $596 \mathrm{nm}$ is aimed at two slits that are separated by $1.90 \times 10^{-5} \mathrm{m} .$ What is the distance from the central band to the first-order yellow band if the screen is $0.600 \mathrm{m}$ from the slits?
In a double-slit experiment, physics students use a laser with $\lambda=632.8 \mathrm{nm} .$ A student places the screen $1.000 \mathrm{m}$ from the slits and finds the first-order bright band $65.5 \mathrm{mm}$ from the central line. What is the slit separation?
Yellow-orange light with a wavelength of 596 nm passes through two slits that are separated by $2.25 \times 10^{-5} \mathrm{m}$ and makes an interference pattern on a screen. If the distance from the central line to the first-order yellow band is $2.00 \times 10^{-2} \mathrm{m}$, how far is the screen from the slits?
In the situation in Example Problem 2, what would be the thinnest film that would createa reflected red $(\lambda=635 \mathrm{nm})$ band?
A glass lens has a non reflective coating placed on it. If a film of magnesium fluoride, $n=1.38,$ is placed on the glass, $n=1.52,$ how thick should the layer be to keep yellow green light from being reflected?
A silicon solar cell has a non reflective coating placed on it. If a film of sodium monoxide. $n=1.45,$ is placed on the silicon, $n=3.5,$ how thick should the layer be to keep yellow green light $(\lambda=555 \mathrm{nm})$ from being reflected?
You can observe thin-film interference by dipping a bubble wand into some bubble solution and holding the wand in the air. What is the thickness of the thinnest soap film at which you would see a black stripe if the light illuminating the film has a wavelengthof 521 nm? Use $n=1.33$
What is the thinnest soap film $(n=1.33)$ for which light of wavelength 521 nm will constructively interfere with itself?
Film Thickness Lucien is blowing bubbles and holds the bubble wand up so that a soap film is suspended vertically in the air. What is the second thinnest width of the soap film at which he could expect to see a bright stripe if the light illuminating the film has a wavelength of 575 nm? Assume the soap solution has an index of refraction of 1.33
Two very narrow slits are cut close to each other in a large piece of cardboard. They are illuminated by monochromatic red light. A sheet of white paper is placed far from the slits, and a pattern of bright and dark bands is seen on the paper. Describe how a wave behaves when it encounters a slit, and explain why some regions are bright while others are dark.
Sketch the pattern described in problem 11
Sketch what happens to the pattern in problem 11 when the red light is replaced by blue light.
A plastic reflecting film ( $n=1.83$ ) is placed on an auto glass window $(n=1.52)$a. What is the thinnest film that will reflect yellow green light?b. Unfortunately, a film this thin cannot be manufactured. What is the next-thinnest film that will produce the same effect?
The equation for wavelength from a double-slit experiment uses the simplification that $\theta$ is small so that $\sin \theta \approx$ tan $\theta .$ Up to what angle is this a good approximation when your data has two significant figures? Would the maximum angle for a valid approximation increase or decrease as you increase the precision of your angle measurement?