Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 37.2, Problem 37.1QQ
Suppose the slit width in Figure 37.4 is made half as wide. Does the central bright fringe (a) become wider, (b) remain the same, or (c) become narrower?
Figure 37.4 (a) Geometry for analyzing the Fraunhofer diffraction pattern of a single slit. (Drawing not to scale.) (b) Simulation of a single-slit Fraunhofer diffraction pattern.
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Light with wavelength i passes through a narrow slit of width w and is seen on a screen which
is located at a distance D in front of the slit. The first minimum of the diffraction pattern is at
distance d from the middle of the central maximum. Calculate the wavelength of light if D=2.5
VAD. Give your answer in nanometprs.
m, d=1 mm and w =
Answer:
Choose...
Light of wavelength 588.2 nm illuminates a slit of width 0.63 mm.
(a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.86 mm from the central maximum?
(b) Calculate the width of the central maximum.
Step 1
(a) As shown in the figure, dark bands or minima occur where sin 0 = m(2/a). For the first minimum, m = 1 and the distance from the center of the central
maximum to the first minimum is y₁ = L tan 8, where L is the distance of the viewing screen from the slit.
32 sin dark = 22/a
31 sin dark = λ/a
HE
0
-1 sin dark = -λ/a
-2 sin dark = -22/a
Viewing screen
a
Because is very small, we can use the approximation tan sin 0 = m(2/a). Substituting the approximation and solving for the distance to the screen, we have
6.3 x 10 m
³ m ) (₁
L =
= y ₁ ( ² ) =
x 10-3 m
x 10-⁹ m
m.
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.
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Chapter 37 Solutions
Physics for Scientists and Engineers
Ch. 37.2 - Suppose the slit width in Figure 37.4 is made half...Ch. 37.3 - Cats eyes have pupils that can be modeled as...Ch. 37.3 - Suppose you are observing a binary star with a...Ch. 37.4 - Ultraviolet light of wavelength 350 nm is incident...Ch. 37.6 - A polarizer for microwaves can be made as a grid...Ch. 37.6 - You are walking down a long hallway that has many...Ch. 37 - Heliumneon laser light ( = 632.8 nm) is sent...Ch. 37 - From Equation 37.2, find an expression for the...Ch. 37 - Light of wavelength 540 nm passes through a slit...Ch. 37 - In Figure 37.7, show mathematically how many...
Ch. 37 - Assume light of wavelength 650 nm passes through...Ch. 37 - What If? Suppose light strikes a single slit of...Ch. 37 - A diffraction pattern is formed on a screen 120 cm...Ch. 37 - Coherent light of wavelength 501.5 nm is sent...Ch. 37 - The objective lens of a certain refracting...Ch. 37 - Yellow light of wavelength 589 nm is used to view...Ch. 37 - What is the approximate size of the smallest...Ch. 37 - A heliumneon laser emits light that has a...Ch. 37 - To increase the resolving power of a microscope,...Ch. 37 - Prob. 14PCh. 37 - Impressionist painter Georges Seurat created...Ch. 37 - Narrow, parallel, glowing gas-filled tubes in a...Ch. 37 - Consider an array of parallel wires with uniform...Ch. 37 - Three discrete spectral lines occur at angles of...Ch. 37 - A grating with 250 grooves/mm is used with an...Ch. 37 - Show that whenever white light is passed through a...Ch. 37 - Light from an argon laser strikes a diffraction...Ch. 37 - A wide beam of laser light with a wavelength of...Ch. 37 - You are working as a demonstration assistant for a...Ch. 37 - Prob. 24PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Why is the following situation impossible? A...Ch. 37 - The critical angle for total internal reflection...Ch. 37 - For a particular transparent medium surrounded by...Ch. 37 - Prob. 31PCh. 37 - An unpolarized beam of light is incident on a...Ch. 37 - In a single-slit diffraction pattern, assuming...Ch. 37 - Laser light with a wavelength of 632.8 nm is...Ch. 37 - Prob. 35APCh. 37 - Two motorcycles separated laterally by 2.30 m are...Ch. 37 - The Very Large Array (VLA) is a set of 27 radio...Ch. 37 - Two wavelengths and + (with ) are incident on...Ch. 37 - Review. A beam of 541-nm light is incident on a...Ch. 37 - Prob. 40APCh. 37 - Prob. 41APCh. 37 - Prob. 42APCh. 37 - A pinhole camera has a small circular aperture of...Ch. 37 - Prob. 44APCh. 37 - Prob. 45APCh. 37 - (a) Light traveling in a medium of index of...Ch. 37 - The intensity of light in a diffraction pattern of...Ch. 37 - Prob. 48APCh. 37 - Two closely spaced wavelengths of light are...Ch. 37 - A spy satellite can consist of a large-diameter...Ch. 37 - Prob. 51CPCh. 37 - In Figure P37.52, suppose the transmission axes of...Ch. 37 - Consider a light wave passing through a slit and...
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- Table P35.80 presents data gathered by students performing a double-slit experiment. The distance between the slits is 0.0700 mm, and the distance to the screen is 2.50 m. The intensity of the central maximum is 6.50 106 W/m2. What is the intensity at y = 0.500 cm? TABLE P35.80arrow_forwardIn the double-slit arrangement of Figure P36.13, d = 0.150 mm, L = 140 cm, = 643 nm. and y = 1.80 cm. (a) What is the path difference for the rays from the two slits arriving at P? (b) Express this path difference in terms of . (c) Does P correspond to a maximum, a minimum, or an intermediate condition? Give evidence for your answer. Figure P36.13arrow_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_forward
- Why is monochromatic light used in the double slit experiment? What would happen if white light were used?arrow_forwardIf 580-nm light falls on a slit 0.05 mm wide, what is the full angular width of the centraldiffraction peak? A single slit 1.0 mm wide is illuminated by 450-nm light. What is the width of the centralmaximum (in cm) in the diffraction pattern on a screen 7.0 m away?arrow_forwardConsider a 505-nm light falling on a single slit of width 1.1 µm. Hint a. At what angle is the first minimum of the diffraction intensity? First minimum is at deg. b. Will there be a second minimum? Yes. No. Not enough information.arrow_forward
- The width of the central peak in a single-slit diffraction pattern is 5.0 mm. The wavelength of the light is 600. nm, and the screen is 1.9 m from the slit. (a.) What is the width of the slit in microns? (D= ?) (b.) What is the ratio of the intensity at 4.2mm from the center of the pattern to the intensity at the center of the pattern? (I/I0= ?)arrow_forwardThe figure below shows the standard setup for Young's double-slit experiment. The spacing between the slits is d, and the screen is a distance L away from the slits. The derivation of the two-slit interference conditions assumes that the two lines of sight to a point P are parallel, since L>d, allowing us to approximate the path length difference as 42= dsıne. How 3.00 cm, d = 0.740 mm, and 0 = good is this approximation? Suppose that L = approximation for a case where L is closer to d.) 9.00°. (Under normal experimental conditions, L/d would be much larger than this, but we want to test the Use geometry and trigonometry to compute the value for the actual path length difference A2. Enter your answer as a positive value. 337.3 m Incorrect. Tries 2/100 Previous Tries Submit Answer By what percentage does this value differ from the approximation Al=dsint? (Enter your answer as a positive number, without the percent sign. Be sure to keep lots of digits in your calculations!) Submit Answer…arrow_forwardIn a diffraction experiment set-up, second maximum is located 15 mm from the central bright fringe. A 668-nm monochromatic light is allowed to pass through a single slit which is 4.5 meters away from the screen. What must be the width of this single slit?arrow_forward
- How much diffraction spreading does a light beam undergo? One quantitative answer is the full width at half maximum of the central maximum of the single-slit Fraunhofer diffraction pattern. You can evaluate this angle of spreading in this problem. (a) as shown, define φ = πa sin φ/λ and show that at the point where I = 0.5Imax we must have φ = √2 sin φ. (b) Let y1 = sin φ and y2 = φ = /√2. Plot y1 and y2 on the same set of axes over a range from φ = 1 rad to φ = π/2 rad. Determine φ from the point of intersection of the two curves. (c) Then show that if the fraction λ/a is notlarge, the angular full width at half maximum of the central diffraction maximum is θ = 0.885λ/a. (d) What If? Another method to solve the transcendental equation φ = √2 sin φ in part (a) is to guess a first value of φ, use a computer or calculator to see how nearly it fits, and continue to update your estimate until the equation balances. How many steps(iterations) does this process take?arrow_forwardWhen performing a Young's double slit experiment, what is the required separation distance between the two slits (in micrometers) to cause 534 nm light to have its first order maximum at an angle of 22.1 degrees? Your Answer:arrow_forwardProblem 2. A) A Michelson interferometer uses light of wavelength 500 nm. The irradiance of the beam exiting the laser is IL. What are the possible differences in the lengths of the arms of the interferometer when the irradiance at the detector is IL/3? B) Young's Double slit experiment is performed with HeNe laser wavelength 632.8 nm. The screen is 2 m from the slits and the slit separation is 0.2 mm. Find the distance of the 3th bright fringe from the center of the interference pattern on the screen (call the central bright fringe the "Oth" fringe).arrow_forward
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