College Physics (10th Edition)
10th Edition
ISBN: 9780321902788
Author: Hugh D. Young, Philip W. Adams, Raymond Joseph Chastain
Publisher: PEARSON
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Chapter 26, Problem 49GP
Suppose you illuminate two thin slits by monochromatic coherent light in air and find that they produce their first interference minima at ±35.20° on either side of the central bright spot. You then immerse these slits in a transparent liquid and illuminate them with the same light. Now you find that the first minima occur at ±19.46° instead What is the index of refraction of this liquid?
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Suppose you illuminate two thin slits by monochromatic coherent light in air and find that they produce their first interference minima at ±35.20° on either side of the central bright spot. You then immerse these slits in a transparent liquid and illuminate them with the same light. Now you find that the first minima occur at ±19.46° instead. What is the index of refraction of this liquid?
One way to determine the index of refraction of a gas is to use an interferometer. As shown below, one of the beams of an interferometer passes through a glass container that has a length of L = 1.8 cm. Initially the
glass container is a vacuum. When gas is slowly allowed into the container, a total of 7571 dark fringes move past the reference line. The laser has a wavelength of 687 nm (this is the wavelength when the light from
the laser is moving through a vacuum).
Laser
Mirror
Glass Container
Beam Splitter
Diffraction Pattern
Mirror
A.) Determine how many wavelengths will fit into the glass container when it is a vacuum. Since the
light passes through the container twice, you need to determine how many wavelengths will fit into a
glass container that has a length of 2L.
number of wavelengths (vacuum) =
B.) The number of dark fringes is the difference between the number of wavelengths that fit in the
container (length of 2L) when it has gas and the number of wavelengths that fit in…
One way to determine the index of refraction of a gas is to use an interferometer. As shown below, one of the beams of an interferometer passes through a glass container that has a length of L = 1.8 cm. Initially the glass container is a vacuum. When gas is slowly allowed into the container, a total of 6894 dark fringes move past the reference line. The laser has a wavelength of 635 nm (this is the wavelength when the light from the laser is moving through a vacuum).
A.) Determine how many wavelengths will fit into the glass container when it is a vacuum. Since the light passes through the container twice, you need to determine how many wavelengths will fit into a glass container that has a length of 2L.number of wavelengths (vacuum) =
B.) The number of dark fringes is the difference between the number of wavelengths that fit in the container (length of 2L) when it has gas and the number of wavelengths that fit in the container (length of 2L) when it is a vacuum. Use this knowledge to…
Chapter 26 Solutions
College Physics (10th Edition)
Ch. 26 - Could an experiment similar to Youngs two-slit...Ch. 26 - You shine monochromatic light on two narrow slits...Ch. 26 - Would the headlights of a distant car form a...Ch. 26 - If a two-slit interference experiment were done...Ch. 26 - Prob. 6CQCh. 26 - Prob. 7CQCh. 26 - Around harbors, where oil from boat engines is on...Ch. 26 - What happens to the width of the central bright...Ch. 26 - A very thin soap film (n = 1.33), whose thickness...Ch. 26 - Suppose monochromatic light with a wavelength A...
Ch. 26 - Optical telescopes having a principal mirror only...Ch. 26 - Two sources of waves are at A and B in Figure...Ch. 26 - Two sources of waves are at A and B in Figure...Ch. 26 - To obtain the greatest resolution from a...Ch. 26 - A monochromatic beam of laser light falls on a...Ch. 26 - When a thin oil film spreads out on a puddle...Ch. 26 - A laser beam of wavelength 500 nm is shone through...Ch. 26 - A film contains a single thin slit of width a When...Ch. 26 - Light of wavelength A strikes a pane of glass of...Ch. 26 - Two thin parallel slits are a distance d apart....Ch. 26 - Laser light of wavelength A passes through a thin...Ch. 26 - A light oeam st'ikes a pane of glass as shown in...Ch. 26 - Light of wavelength and frequency f passes...Ch. 26 - Prob. 1PCh. 26 - A person with a radio-wave receiver starts out...Ch. 26 - Radio interference. Two radio antennas A and B...Ch. 26 - Two speakers that are 10.0 m apart produce...Ch. 26 - Suppose that the situation is the same as in the...Ch. 26 - Coherent light of wavelength 525 nm passes through...Ch. 26 - Coherent light from a sodium-vapor lamp is passed...Ch. 26 - Young's experiment is performed with light of...Ch. 26 - Coherent light of frequency 6 32 1014 Hz passes...Ch. 26 - Coherent light with wavelength 600 nm passes...Ch. 26 - Two slits spaced 0.450 mm apart are placed 75.0 cm...Ch. 26 - Coherent light that contains two wavelengths 660...Ch. 26 - Two thin parallel slits that are 0.0116 mm apart...Ch. 26 - The walls of a soap bubble have about the same...Ch. 26 - What is the thinnest soap film (excluding the case...Ch. 26 - A thin film of polystyrene of refractive index...Ch. 26 - Conserving energy. The lead architect on the...Ch. 26 - Nonglare glass. When viewing a piece of art that...Ch. 26 - The lenses of a particular set of binoculars have...Ch. 26 - A plate of glass 9.00 cm long is placed in contact...Ch. 26 - Two rectangular pieces of plane glass are laid one...Ch. 26 - A researcher measures the thickness of a layer of...Ch. 26 - Compact disc player. A compact disc (CD) is read...Ch. 26 - A beam of laser light of wavelength 632.8 nm fails...Ch. 26 - Parallel rays of green mercury light with a...Ch. 26 - Parallel light rays with a wavelength of 600 nm...Ch. 26 - Monochromatic light from a distant source is...Ch. 26 - Red light of wavelength 633 nm from a helium-neon...Ch. 26 - Light of wavelength 633 nm from a distant source...Ch. 26 - Doorway diffraction. Diffraction occurs for all...Ch. 26 - Light of wavelength 585 nm falls on a slit 0 0666...Ch. 26 - A glass sheet measuring 10.0 cm 25.0 cm is...Ch. 26 - A laser beam of unknown wavelength passes through...Ch. 26 - A laser beam of wavelength 600.0 nm is incident...Ch. 26 - When laser light of wavelength 632.8 nm passes...Ch. 26 - A diffraction grating has 5580 lines/cm When a...Ch. 26 - Monochromatic light is at normal incidence on a...Ch. 26 - Set Up: The maxima are located by dsin= m, where d...Ch. 26 - Light of wavelength 631 nm passes through a...Ch. 26 - If a diffraction grating produces a third-order...Ch. 26 - A converging lens 7.20 cm in diameter has a focal...Ch. 26 - A reflecting telescope is used to observe two...Ch. 26 - Two satellites at an altitude of 1200 km are...Ch. 26 - Resolution of telescopes. Due to blurring caused...Ch. 26 - Resolution of the eye, I. Even if the lenses of...Ch. 26 - Resolution of the eye, II. The maximum resolution...Ch. 26 - Spy satellites? Assume that a spy satellite in...Ch. 26 - Two identical audio speakers connected to the same...Ch. 26 - Suppose you illuminate two thin slits by...Ch. 26 - Coating eyeglass lenses. Eyeglass lenses can be...Ch. 26 - Sensitive eyes. You have just put some medical...Ch. 26 - || A wildlife photographer uses a moderate...Ch. 26 - Thickness of human hair. Although we have...Ch. 26 - An oil tanker spills a large amount of oil (n = 1...Ch. 26 - A thin glass slide (n = 1.53) that is 0.485 m...Ch. 26 - Searching for planets around other stars. If an...Ch. 26 - You need a diffraction grating that will disperse...Ch. 26 - Set Up: Interference occurs due to the path...Ch. 26 - A physics student performs Youngs double-slit...Ch. 26 - The professor then adjusts the apparatus. The...Ch. 26 - The professor returns the apparatus to the...Ch. 26 - The professor again returns the apparatus to its...Ch. 26 - The professor once again returns the apparatus to...
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- Monochromatic light of wavelength 530 nm passes through a horizontal single slit of width 1.5 m in an opaque plate. A screen of dimensions 2.0m2.0m is 1.2 m away from the slit. (a) Which way is the diffraction pattern spread out on the screen? (b) What are the angles of the minima with respect to the center? (c) What are the angles of the maxima? (d) How wide is the central bright fringe on the screen? (e) How wide is the next bright fringe on the screen?arrow_forwardA Fraunhofer diffraction pattern is produced on a screen located 1.00 m from a single slit. If a light source of wavelength 5.00 107 m is used and the distance from the center of the central bright fringe to the first dark fringe is 5.00 103 m, what is the slit width? (a) 0.010 0 mm (b) 0.100 mm (c) 0.200 mm (d) 1.00 mm (e) 0.005 00 mmarrow_forwardIn Figure P27.7 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4?arrow_forward
- (a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 m. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.arrow_forwardCoherent light rays of wavelength strike a pair of slits separated by distance d at an angle 1, with respect to the normal to the plane containing the slits as shown in Figure P27.14. The rays leaving the slits make an angle 2 with respect to the normal, and an interference maximum is formed by those rays on a screen that is a great distance from the slits. Show that the angle 2 is given by 2=sin1(sin1md) where m is an integer.arrow_forwardFigure P36.53 shows two thin glass plates separated by a wire with a square cross section of side length w, forming an air wedge between the plates. What is the edge length w of the wire if 42 dark fringes are observed from above when 589-nm light strikes the wedge at normal incidence? FIGURE P36.53arrow_forward
- In Figure P36.10 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4? Figure P36.10arrow_forwardA monochromatic light beam coming from a point source illuminates two parallel horizontal slits. The center of the two slits is a = 0.80 mm, as illustrated in the figure. An interference pattern is produced on a target at 50 cm. In this pattern, the dark and light fringes are equally spaced. The distance y1 is 0.304 mm.Calculate the wavelength of the incident light.arrow_forwardPlease asaparrow_forward
- The red light of the He-Ne laser (λ0 = 632.8 nm) is reduced to two very narrow horizontal slits with a distance of 0.200 mm between them. Interference fringes are obtained on the white screen at a distance of 1.00 m.a) how far below and above the Center do the first dark spots occur? Give your results in mm and radians.b) how many mm far from the center is the 5th luminous Eaves, including the zero luminous Eaves in the center?arrow_forwardOne leg of a Michelson interferometer contains an evacuated cylinder of length L, =0.30m having glass plates on each end. A gas is slowly leaked into the cylinder until a pressure of 1 atm is reached. If 140 bright fringes pass on the screen when light of wavelength A=440nm is used, what is n, the index of refraction of the gas? State your answer to the nearest 0.000001 ( one part per million).arrow_forwardThe Michelson interferometer can be used to measure the index of refraction of a gas by placing an evacuated transparent tube in the light path along one arm of the device. Fringe shifts occur as the gas is slowly added to the tube. Assume 580-nm light is used, the tube is 5.40 cm long, and 152 fringe shifts occur as the pressure of the gas in the tube increases to atmospheric pressure. What is the index of refraction of the gas? Hint: The fringe shifts occur because the wavelength of the light changes inside the gas-filled tube. (Give your answer to five decimal places.) 4.0arrow_forward
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