UNIVERSITY PHYSICS,VOL.3 (OER)
17th Edition
ISBN: 2810020283905
Author: OpenStax
Publisher: XANEDU
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Chapter 3, Problem 28P
Shown below is a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, numerous bright spots appear, called fringes. Show that, for small angles (where
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This figure shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. It can be shown that, for small angles (where sin ? ?, with ? in radians), the distance between fringes is given by Δy = x?/d. Using this result, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.110 mm.
=___nm
In the case of diffraction by a rectangular slit of width a, it can be proved that the amplitude distribution as a function of the angular position θ is given by A = A₀ sin(u)/u, where A₀ is a constant, u = (πa sin θ)/λ and the function sin(u)/u must be replaced by 1 if u=0. As seen in class, the intensity minima occur for sin θ = nλ, n=1, 2, 3, ... (a) What is the equation that determines the positions of the intensity maxima? (b) What is the angular position θ₁ of the first maximum, excluding the central maximum? Please note: as a rule, transcendent equations can only be solved numerically.
In the case of diffraction by a rectangular slit of width a, it can be proved that the amplitude distribution as a function of the angular position θ is given by A = A₀ sin(u)/u, where A₀ is a constant, u = (πa sin θ)/λ and the function sin(u)/u must be replaced by 1 if u=0. As seen in class, the intensity minima occur for sin θ = nλ, n=1, 2, 3, ... (a) What is the equation that determines the positions of the intensity maxima? (b) What is the angular position θ₁ of the first maximum, excluding the central maximum
( ) (a) u = nπ, n = 1, 2, 3, … (b) sen θ₁ = λ/a
( ) (a) u = nπ/2, n = 1, 3, 5, … (b) sen θ₁= λ/2a
( ) (a) tg u - u = 0 (b) sen θ₁ = 4,49341 λ/πa
( ) (a) tg u - u = 0 (b) sen θ₁= 2λ/πa
( ) (a) tg u - u = 0 (b) sen θ₁ = 3λ/πa
( ) (a) tg u - u = 0 (b) sen θ₁ = 2λ/a
( ) (a) tg u - u = 0 (b) sen θ₁ = 3λ/a
( ) (a) tg u - u = 0 (b) sen θ₁ = 4,49341 λ/a
( ) (a) cos u - u = 0 (b) sen θ₁ = 0,7391 λ/πa
( ) (a) cos u - u = 0 (b)…
Chapter 3 Solutions
UNIVERSITY PHYSICS,VOL.3 (OER)
Ch. 3 - Check Your Understanding In the system used in the...Ch. 3 - Check Your Understanding Going further with...Ch. 3 - Check Your Understanding Although m, the number of...Ch. 3 - Young’s double-slit experiment breaks a single...Ch. 3 - Is it possible to create a experimental setup in...Ch. 3 - Why won’t two small sodium lamps, held close...Ch. 3 - Suppose you use the same double slit to perform...Ch. 3 - Why is monochromatic light used in the double slit...Ch. 3 - What effect does increasing the wedge angle have...Ch. 3 - How is the difference in paths taken by two...
Ch. 3 - Is there a phase change in the light reflected...Ch. 3 - In placing a sample on a microscope slide, a glass...Ch. 3 - Answer the above question if the fluid between the...Ch. 3 - While contemplating the food value of a slice of...Ch. 3 - An inventor notices that a soap bubble is dark at...Ch. 3 - A nonreflective coating like the one described in...Ch. 3 - Why is it much more difficult to see interference...Ch. 3 - Describe how a Michelson interferometer can be...Ch. 3 - At what angle is the first-order maximum for...Ch. 3 - Calculate the angle for the third-order maximum of...Ch. 3 - What is the separation between two slits for which...Ch. 3 - Find the distance between two slits that produces...Ch. 3 - Calculate the wavelength of light that has its...Ch. 3 - What is the wavelength of light falling on double...Ch. 3 - At what angle is the fourth-order maximum for the...Ch. 3 - What is the highest-order maximum for 400-nm light...Ch. 3 - Find the largest wavelength of light falling on...Ch. 3 - What is the smallest separation between two slits...Ch. 3 - (a) What is the smallest separation between two...Ch. 3 - (a) If the first-order maximum for monochromatic...Ch. 3 - Shown below is a double slit located a distance x...Ch. 3 - Using the result of the preceding problem, (a)...Ch. 3 - Using the result of the problem two problems...Ch. 3 - In a double-slit experiment, the fifth maximum is...Ch. 3 - The source in Young’s experiment emits at two...Ch. 3 - If 500-nm and 650-nm light illuminates two slits...Ch. 3 - Red light of wavelength of 700 nm falls on a...Ch. 3 - Ten narrow slits are equally spaced 0.25 mm apart...Ch. 3 - The width of bright fringes can be calculated as...Ch. 3 - For a three-slit interference pattern, find the...Ch. 3 - What is the angular width of the central fringe of...Ch. 3 - A soap bubble is 100 nm thick and illuminated by...Ch. 3 - An oil slick on water is 120 nm thick and...Ch. 3 - Calculate the minimum thickness of an oil slick on...Ch. 3 - Find the minimum thickness of a soap bubble that...Ch. 3 - A film of soapy water (n=1.33) on top of a plastic...Ch. 3 - What are the three smallest non-zero thicknesses...Ch. 3 - Suppose you have a lens system that is to be used...Ch. 3 - (a) As a soap bubble thins it becomes dark,...Ch. 3 - To save money on making military aircraft...Ch. 3 - A Michelson interferometer has two equal arms. A...Ch. 3 - What is the distance moved by the traveling mirror...Ch. 3 - When the traveling mirror of a Michelson...Ch. 3 - In a Michelson interferometer, light of wavelength...Ch. 3 - A chamber 5.0 cm long with flat, parallel windows...Ch. 3 - For 600-nm wavelength light and a slit separation...Ch. 3 - If the light source in the preceding problem is...Ch. 3 - Red light (=710.nm) illuminates double slits...Ch. 3 - Two sources as in phase and emit waves with =0.42...Ch. 3 - Two slits 4.0106 m apart are illuminated by light...Ch. 3 - Suppose that the highest order fringe that can be...Ch. 3 - The interference pattern of a He-Ne laser light...Ch. 3 - Young’s double-slit experiment is performed...Ch. 3 - A double-slit experiment is to be set up so that...Ch. 3 - An effect analogous to two-slit interference can...Ch. 3 - A hydrogen gas discharge lamp emits visible light...Ch. 3 - Monochromatic light of frequency 5.51014 Hz falls...Ch. 3 - Eight slits equally separated by 0.149 mm is...Ch. 3 - Eight slits equally separated by 0.149 mm is...Ch. 3 - A transparent film of thickness 250 nm and index...Ch. 3 - An intensity minimum is found for 450 nm light...Ch. 3 - A thin film with n=1.32 is surrounded by air. What...Ch. 3 - Repeat your calculation of the previous problem...Ch. 3 - After a minor oil spill, a think film of oil...Ch. 3 - A microscope slide 10 cm long is separated from a...Ch. 3 - Suppose that the setup of the preceding problem is...Ch. 3 - A thin wedge filled with air is produced when two...Ch. 3 - Two identical pieces of rectangular plate glass...Ch. 3 - Two microscope slides made of glass are...Ch. 3 - A good quality camera “lens” is actually a system...Ch. 3 - Constructive interference is observed from...Ch. 3 - A soap bubble is blown outdoors. What colors...Ch. 3 - A Michelson interferometer with a He-Ne laser...Ch. 3 - An experimenter detects 251 fringes when the...Ch. 3 - A Michelson interferometer is used to measure the...Ch. 3 - A 5.08-cm-long rectangular glass chamber is...Ch. 3 - Into one arm of a Michelson interferometer, a...Ch. 3 - The thickness of an aluminum foil is measured...Ch. 3 - The movable mirror of a Michelson interferometer...Ch. 3 - In a thermally stabilized lab, a Michelson...Ch. 3 - A 65-fringe shift results in a Michelson...Ch. 3 - Determine what happens to the double-slit...Ch. 3 - Fifty-one narrow slits are equally spaced and...Ch. 3 - A film of oil on water will appear dark when it is...Ch. 3 - Figure 3.14 shows two glass slides illuminated by...Ch. 3 - Figure 3.14 shows two 7.50-cm-long glass slides...Ch. 3 - A soap bubble is 100 nm thick and illuminated by...Ch. 3 - An oil slick on water is 120 nm thick and...
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