Fundamentals of Physics
10th Edition
ISBN: 9781118230718
Author: David Halliday
Publisher: Wiley, John & Sons, Incorporated
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Textbook Question
Chapter 36, Problem 95P
SSM If you double the width of a single slit, the intensity of the central maximum of the diffraction pattern increases by a factor of 4, even though the energy passing through the slit only doubles. Explain this quantitatively.
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Students have asked these similar questions
In a certain crystal the spacing between crystal planes is 0.165 nm. (a) If you shine a beam of x rays of wavelength 0.124 nm on this crystal, for what angle between the beam and the crystal planes does the first strong interference maximum occur? (b) For what larger angles (if any) do strong interference maxima occur?
Coherent electromagnetic waves with wavelength λ = 500 nm pass through two identical slits. The width of each slit is a, and the distance between the centers of the slits is d = 9.00 mm. (a) What is the smallest possible width a of the slits if the m = 3 maximum in the interference pattern is not present? (b) What is the next larger value of the slit width for which the m = 3 maximum is absent?
SS-1 Coherent light of wavelength 675 nm passes through a narrow slit of width 0.0143 mm.
The diffraction pattern is projected onto a viewing screen 1.08 m away from the slit. The
intensity of the light at the center of the diffraction pattern is 175 W/m².
(a) Draw a picture of the of situation descried in this problem.
(b) Find the width of the central bright spot on the screen, in centimeters (cm).
(c) Find the distance between the center of the diffraction pattern and the m = 4
minimum on the screen, in cm.
(d) What is the intensity at a point on the screen 13.5 cm from the central maximum?
Chapter 36 Solutions
Fundamentals of Physics
Ch. 36 - You are conducting a single-slit diffraction...Ch. 36 - In a single-slit diffraction experiment, the top...Ch. 36 - For three experiments, Fig. 36-30 gives the...Ch. 36 - For three experiments, Fig. 36-31 gives versus...Ch. 36 - Figure 36-32 shows four choices for the...Ch. 36 - Prob. 6QCh. 36 - At night many people see rings called entoptic...Ch. 36 - a For a given diffraction grating, does the...Ch. 36 - Figure 36-33 shows a red line and a green line of...Ch. 36 - For the situation of Question 9 and Fig. 36-33, if...
Ch. 36 - a Figure 36-34a shows the lines produced by...Ch. 36 - Figure 36-35 shows the bright fringes that lie...Ch. 36 - In three arrangements you view two closely spaced...Ch. 36 - For a certain diffraction grating, the ratio /a of...Ch. 36 - GO The distance between the first and fifth minima...Ch. 36 - What must be the ratio of the slit width to the...Ch. 36 - A plane wave of wavelength 590 nm is incident on a...Ch. 36 - In conventional television, signals are broadcast...Ch. 36 - A single slit is illuminated by light of...Ch. 36 - Monochromatic light of wavelength 441 nm is...Ch. 36 - Light of wavelength 633 nm is incident on a narrow...Ch. 36 - Sound waves with frequency 3000 Hz and speed 343...Ch. 36 - SSM ILW A slit 1.00 mm wide is illuminated by...Ch. 36 - GO Manufacturers of wire and other objects of...Ch. 36 - A 0.10-mm-wide slit is illuminated by light of...Ch. 36 - Figure 36-38 gives versus the sine of the angle ...Ch. 36 - Monochromatic light with wavelength 538 nm is...Ch. 36 - In the single-slit diffraction experiment of Fig....Ch. 36 - SSM WWW The full width at half-maximum FWHM of a...Ch. 36 - Babinets principle. A monochromatic beam of...Ch. 36 - a Show that the values of a at which intensity...Ch. 36 - The wall of a large room is covered with acoustic...Ch. 36 - a How far from grains of red sand must you be to...Ch. 36 - The radar system of a navy cruiser transmits at a...Ch. 36 - SSM WWW Estimate the linear separation of two...Ch. 36 - Prob. 22PCh. 36 - SSM The two headlights of an approaching...Ch. 36 - Entoptic halos. If someone looks at a bright...Ch. 36 - ILW Find the separation of two points on the Moons...Ch. 36 - The telescopes on some commercial surveillance...Ch. 36 - If Superman really had x-ray vision at 0.10 nm...Ch. 36 - GO The wings of tiger beetles Fig. 36-41 are...Ch. 36 - a What is the angular separation of two stars if...Ch. 36 - GO Floaters. The floaters you see when viewing a...Ch. 36 - SSM Millimeter-wave radar generates a narrower...Ch. 36 - a A circular diaphragm 60 cm in diameter...Ch. 36 - Prob. 33PCh. 36 - Prob. 34PCh. 36 - Suppose that the central diffraction envelope of a...Ch. 36 - A beam of light of a single wavelength is incident...Ch. 36 - In a double-slit experiment, the slit separation d...Ch. 36 - In a certain two-slit interference pattern, 10...Ch. 36 - Light of wavelength 440 nm passes through a double...Ch. 36 - GO Figure 36-45 gives the parameter of Eq. 36-20...Ch. 36 - GO In the two-slit interference experiment of Fig....Ch. 36 - GO a In a double-slit experiment, what largest...Ch. 36 - SSM WWW a How many bright fringes appear between...Ch. 36 - Perhaps to confuse a predator, some tropical...Ch. 36 - A diffraction grating 20.0 mm wide has 6000...Ch. 36 - Visible light is incident perpendicularly on a...Ch. 36 - SSM ILW A grating has 400 lines/mm. How many...Ch. 36 - A diffraction grating is made up of slits of width...Ch. 36 - SSM WWW Light of wavelength 600 nm is incident...Ch. 36 - With light from a gaseous discharge tube incident...Ch. 36 - GO A diffraction grating having 180 lines/mm is...Ch. 36 - GO A beam of light consisting of wavelengths from...Ch. 36 - Prob. 53PCh. 36 - Derive this expression for the intensity pattern...Ch. 36 - SSM ILW A source containing a mixture of hydrogen...Ch. 36 - a How many rulings must a 4.00-cm-wide diffraction...Ch. 36 - Light at wavelength 589 nm from a sodium lamp is...Ch. 36 - A grating has 600 rulings/mm and is 5.0 mm wide. a...Ch. 36 - A diffraction grating with a width of 2.0 cm...Ch. 36 - Prob. 60PCh. 36 - With a particular grating the sodium doublet...Ch. 36 - A diffraction grating illuminated by monochromatic...Ch. 36 - Assume that the limits of the visible spectrum are...Ch. 36 - What is the smallest Bragg angle for x rays of...Ch. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - If first-order reflection occurs in a crystal at...Ch. 36 - X rays of wavelength 0.12 nm are found to undergo...Ch. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Consider a two-dimensional square crystal...Ch. 36 - An astronaut in a space shuttle claims she can...Ch. 36 - SSM Visible light is incident perpendicularly on a...Ch. 36 - A beam of light consists of two wavelengths,...Ch. 36 - SSM In a single-slit diffraction experiment, there...Ch. 36 - GO A double-slit system with individual slit...Ch. 36 - SSM A diffraction grating has resolving power R =...Ch. 36 - The pupil of a persons eye has a diameter of 5.00...Ch. 36 - Prob. 81PCh. 36 - A grating with d = 1.50 m is illuminated at...Ch. 36 - SSM In two-slit interference, if the slit...Ch. 36 - GO In a two-slit interference pattern, what is the...Ch. 36 - A beam of light with a narrow wavelength range...Ch. 36 - If you look at something 40 m from you, what is...Ch. 36 - Two yellow flowers are separated by 60 cm along a...Ch. 36 - In a single-slit diffraction experiment, what must...Ch. 36 - A diffraction grating 3.00 cm wide produces the...Ch. 36 - A single-slit diffraction experiment is set up...Ch. 36 - A diffraction grating has 8900 slits across 1.20...Ch. 36 - In an experiment to monitor the Moons surface with...Ch. 36 - In June 1985, a laser beam was sent out from the...Ch. 36 - A diffraction grating 1.00 cm wide has 10 000...Ch. 36 - SSM If you double the width of a single slit, the...Ch. 36 - When monochromatic light is incident on a slit...Ch. 36 - A spy satellite orbiting at 160 km above Earths...Ch. 36 - Suppose that two points are separated by 2.0 cm....Ch. 36 - A diffraction grating has 200 lines/mm. Light...Ch. 36 - A diffraction grating has 200 rulings/mm, and it...Ch. 36 - Prob. 101PCh. 36 - Monochromatic light wavelength = 450 nm is...Ch. 36 - Light containing a mixture of two wavelengths, 500...Ch. 36 - Prob. 104PCh. 36 - Show that a grating made up of alternately...Ch. 36 - Light of wavelength 500 nm diffracts through a...Ch. 36 - If, in a two-slit interference pattern, there are...Ch. 36 - White light consisting of wavelengths from 400 nm...Ch. 36 - If we make d = a in Fig. 36-50, the two slits...Ch. 36 - Derive Eq. 36-28, the expression for the...Ch. 36 - Prob. 111PCh. 36 - How many orders of the entire visible spectrum...Ch. 36 - An acoustic double-slit system of slit separation...Ch. 36 - Two emission lines have wavelengths and ,...
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- Problem 1: In a double slit experiment the first minimum for 415 nm violet light is at an angle of 42°. Randomized Variables 2 = 415 nm e = 42 ° Find the distance between the two slits in micrometers. d= 8 9 5 6 sin() cos() tan() 7 HOME cotan() asin() acos() E A 4 atan() acotan() sinh() 1 2 3 cosh() tanh() cotanh() END O Degrees O Radians Vol BACKSPACE DEL CLEAR +arrow_forwardThe full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (a) Show that the intensity drops to one-half the maximum value when sin2 a = a2/2. (b) Verify that a =1.39 rad (about 80°) is a solution to the transcendental equation of (a). (c) Show that the FWHM is u= 2 sin-1(0.443l/a), where a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00l, (e) 5.00l, and (f) 10.0l.arrow_forward..40 Go Figure 36-45 gives the pa- ß (rad) rameter of Eq. 36-20 versus the ßs sine of the angle in a two-slit inter- ference experiment using light of wavelength 435 nm. The vertical axis scale is set by B, = 80.0 rad. What are (a) the slit separation, (b) the total number of interference maxima (count them on both sides of the pattern's center), (c) the smallest angle for a maxima, and (d) the greatest angle for a minimum? Assume that none of the interference maxima are completely eliminated by a diffraction minimum. 0 sin 0 0.5 1 Figure 36-45 Problem 40.arrow_forward
- The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See figure (b).) (a) Does the intensity drop to one-half the maximum value when sin²α = a²/2? (b) Is a = 1.39 rad (about 80°) a solution to the transcendental equation of (a)? (c) Is the FWHM AÐ = 2sin¹(0.442 A/a), where a is the slit width? Calculate the FWHM of the central maximum for slit width (d) 1.17 A, (e) 5.03 A, and (f) 11.7 A. 20 20 Relative intensity 15 10 0.8 0.6 a=2 0.4 0.2 5 05 8 (degrees) (a) 10 15 20 20 Relative intensity 1.0 0.8 0.6 -A0- 0.4 0.2 a= 52 20 15 10 5 0 5 10 15 20 (degrees) (b)arrow_forwardIn the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength λ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is (a) 22 (b) 22 3 (c) 1/17 3 (d) λarrow_forwardThe phase shift between ordinary and extraordinary waves in the plastic and thus the degree of transmission is dependent on both the birefringence An (= no-ne), and the air wavelength 20: Ap= (nod-ned) (2π/20) where the symbols have their usual meaning. If we have a situation whereby, at a particular region in the plastic, for blue light (20= 450nm) the phase shift is 47 and the blue light is not transmitted, at what wavelength will the phase shift be 3r, where the transmission will be a maximum? What will happen to the blue light if we rotate one of the polarisers so that the transmission axes of the two are now parallel?arrow_forward
- X rays of wavelength 0.0850 nm are scattered from the atoms of a crystal. The second-order maximum in the Bragg reflection occurs when the angle θ in Fig is 21.5°. What is the spacing between adjacent atomic planes in the crystal?arrow_forwardWhen an x-ray beam is scattered off the planes of a crystal, the scattered beam creates an interference pattern. This phenomenon is called Bragg scattering. For an observer to measure an interference maximum, two conditions have to be satisfied: 1. The angle of incidence has to be equal to the angle of reflection. 2. The difference in the beam's path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength; that is, 2d sin(0) = mx for m = 1, 2, .... The path difference 2d sin(0) can be determined from the diagram (Figure 1). The second condition is known as the Bragg condition. Figure 1 of 1 d sine d sine Review nstants Part A An x-ray beam with wavelength 0.260 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 20.5 °. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. VE ΑΣΦ ? d = nm…arrow_forwardml (0.0700 nm) 2d 2(0.314 nm) Find the grazing angle corresponding sin e = 0.111 to m = 1, for first-order interference: e = sin-1(0.111) = 6.37° Repeat the calculation for third-order interference (m = 3): mì 3(0.0700 nm) sin e = 2d = 0.334 2(0.314 nm) e = sin(0.334) = 19.5° LEARN MORE REMARKS Notice there is little difference between this kind of problem and a Young's slit experiment. QUESTION If the grazing angle is smaller, the distance between planes in the crystal lattice is: larger. O the same. O smaller. PRACTICE IT Use the worked example above to help you solve this problem. If the spacing between certain planes in a crystal of calcite (CaCO,) is 0.313 nm, find the grazing angles at which first- and third-order interference will occur for x-rays of wavelength 0.0661 nm. 0, = 6.06 82 =| 18.47 EXERCISE HINTS: GETTING STARTED | I'M STUCK! X-rays of wavelength 0.0620 nm are scattered from a crystal with a grazing angle of 11.1°. Assume m = 1 for this process. Calculate the spacing…arrow_forward
- Problem 17: Suppose a 1.8 μm wide slit produces its first minimum for 410 nm violet light.Randomized Variablesλv = 410 nmλv = 410 nmλr = 750 nmw = 1.8 μm Part (a) Calculate the angle at which this occurs for violet light in degrees.Numeric : A numeric value is expected and not an expression.θv = __________________________________________Part (b) Where is the first minimum (in degrees) for 750 nm red light?Numeric : A numeric value is expected and not an expression.θr = __________________________________________arrow_forward2. = A planar dielectric waveguide with the core refractive index n₁ 1.56 and the 1.47 is used to transmit light of wavelength o 750 nm. Suppose cladding index n₂ = = the width of the waveguide is d = 1.0 μm: (a) Determine the critical angle 0c at the interface. (b) Calculate and plot the phase change on reflection o, as a function of angle of incidence in the range 0c < 0arrow_forwardProblem 17: Suppose a 1.8 μm wide slit produces its first minimum for 410 nm violet light.Randomized Variablesλv = 410 nmλr = 750 nmw = 1.8 μm Part (a) Calculate the angle at which this occurs for violet light in degrees.Numeric : A numeric value is expected and not an expression.θv = __________________________________________Part (b) Where is the first minimum (in degrees) for 750 nm red light?Numeric : A numeric value is expected and not an expression.θr = __________________________________________arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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