PHYS 2212 Module 15 Self Assessment Practice Problems

Module 15 Self Assessment Practice Problems

15.2
Coherent light that contains two wavelengths, 660 nm (red) and 470 nm (blue), passes through two narrow slits that are separated by 0.300 mm. Their interference pattern is observed on a screen 4.00 m from the slits. What is the distance on the screen between the first-order bright fringes for the two wavelengths?
Answer: 2.53 mm

15.3
Two slits spaced 0.450 mm apart are placed 75.0 cm from a screen. What is the distance between the second and third dark lines of the interference pattern on the screen when the slits are illuminated with coherent light with a wavelength of 500 nm?
Answer: 0.833 mm

15.4
Coherent light of frequency 6.32 x 10¹⁴ Hz passes through two thin slits and falls on a screen 85.0 cm away. You observe that the third bright fringe occurs at ±3.11 cm on either side of the central bright fringe.
(a) How far apart are the two slits?
(b) At what distance from the central bright fringe will the third dark fringe occur?
Answer: (a) 38.9 µm (b) 2.59 cm

15.5
The walls of a soap bubble have about the same index of refraction as that of plain water, n = 1.33. There is air both inside and outside the bubble.
(a) What wavelength (in air) of visible light is most strongly reflected from a point on a soap bubble where its wall is 290 nm thick? To what color does this correspond?
(b) Repeat part (a) for a wall thickness of 340 nm.
Answer: (a) 514 nm, green (b) 603 nm, orange

15.6
A researcher measures the thickness of a layer of benzene (n = 1.50) floating on water by shining monochromatic light onto the film and varying the wavelength of the light. She finds that light of wavelength 575 nm is reflected most strongly from the film. What does she calculate for the minimum thickness of the film?
Answer: 95.8 nm

15.7
A plastic film with index of refraction 1.70 is applied to the surface of a car window to increase the reflectivity and thus to keep the car’s interior cooler. The window glass has index of refraction 1.52.
(a) What minimum thickness is required if light of wavelength 550 nm in air reflected from the two sides of the film is to interfere constructively?
(b) Coatings as thin as that calculated in part (a) are difficult to manufacture and install. What is the next greater thickness for which constructive interference will also occur?
Answer: (a) 80.9 nm (b) 243 nm

15.8
When viewing a piece of art that is behind glass, one often is affected by the light that is reflected off the front of the glass (called glare), which can make it difficult to see the art clearly. One solution is to coat the outer surface of the glass with a film to cancel part of the glare.
(a) If the glass has a refractive index of 1.62 and you use TiO₂, which has an index of refraction of 2.62, as the coating, what is the minimum film thickness that will cancel light of wavelength 505 nm?
(b) If this coating is too thin to stand up to wear, what other thickness would also work? Find only the three thinnest ones.
Answer: (a) 96.4 nm (b) 193 nm, 289 nm, 385 nm

15.9
An oil slick on water is 120 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength), given its index of refraction is 1.40?
Answer: Red, 672 nm

15.10
To save money on making military aircraft invisible to radar, an inventor decides to coat them with a nonreflective material having an index of refraction of 1.20, which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers.
(a) What thickness should the coating be to inhibit the reflection of 4.00-cm wavelength radar?
(b) What is unreasonable about this result? Which assumptions are unreasonable or inconsistent?
Answer: 8.3 mm