Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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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
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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
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Chapter 37 Solutions
Physics for Scientists and Engineers with Modern Physics
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 - Prob. 37.6QQCh. 37 - Prob. 1PCh. 37 - Prob. 2PCh. 37 - Prob. 3PCh. 37 - In Figure 37.7, show mathematically how many...
Ch. 37 - Prob. 5PCh. 37 - What If? Suppose light strikes a single slit of...Ch. 37 - Prob. 7PCh. 37 - Coherent light of wavelength 501.5 nm is sent...Ch. 37 - Prob. 9PCh. 37 - Prob. 10PCh. 37 - What is the approximate size of the smallest...Ch. 37 - Prob. 12PCh. 37 - Prob. 13PCh. 37 - Prob. 14PCh. 37 - Impressionist painter Georges Seurat created...Ch. 37 - Prob. 16PCh. 37 - Consider an array of parallel wires with uniform...Ch. 37 - Prob. 18PCh. 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 - Prob. 22PCh. 37 - You are working as a demonstration assistant for a...Ch. 37 - Prob. 24PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 28PCh. 37 - Prob. 29PCh. 37 - Prob. 30PCh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33APCh. 37 - Laser light with a wavelength of 632.8 nm is...Ch. 37 - Prob. 35APCh. 37 - Prob. 36APCh. 37 - Prob. 37APCh. 37 - Prob. 38APCh. 37 - Prob. 39APCh. 37 - Prob. 40APCh. 37 - Prob. 41APCh. 37 - Prob. 42APCh. 37 - Prob. 43APCh. 37 - Prob. 44APCh. 37 - Prob. 45APCh. 37 - Prob. 46APCh. 37 - Prob. 47APCh. 37 - Prob. 48APCh. 37 - Two closely spaced wavelengths of light are...Ch. 37 - Prob. 50CPCh. 37 - Prob. 51CPCh. 37 - In Figure P37.52, suppose the transmission axes of...Ch. 37 - Prob. 53CP
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- 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_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_forwardWhy is monochromatic light used in the double slit experiment? What would happen if white light were used?arrow_forward
- If 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_forwardcan you explain how the answer for the last question is 6.248966E-7?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
- Suppose a laser shines through a double slit with separation d. The patern on the screen is .9 m from the slits. The distance between the two bright fringes (△y) is measured in mm. See the attatched plot. What is the wave number for the light in inverse nanometers?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_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_forward
- When 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_forwardHow 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_forwardLight of wavelength 470 nm passes through a double slit, yielding a diffraction pattern whose graph of intensity I versus angular position e is shown in the figure. Calculate (a) the slit width and (b) the slit separation. If Im = 7.1 mW/cm2 what are the intensities of the (c) m 1 and (d) m = 2 interference fringes? 9. e (degrees) Units (a) Number 4496 Units (b) Number 1.798e4 nm UnitsmW/m^2 (c) Number 5.75e4 UnitsmW/m^2 (d) Number | 1.15e5 Intensity (mW/cm²)arrow_forward
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