Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 27, Problem 14P
Coherent light rays of wavelength λ strike a pair of slits separated by distance d at an angle θ1, 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 θ2 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 θ2 is given by
where m is an integer.
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Students have asked these similar questions
The figure shows the interference pattern that appears on a distant screen when coherent light is incident on a mask with two identical, very narrow slits. Points P and Q are maxima; Point R is a minimum. The wavelength of the light that created the interference pattern is λ=678nm, the two slites are separated by rm d=6 μm, and the distance from the slits to the center of the screen is L=80cm . The difference in path length at a point on the screen is Δs=|s1−s2|, where s1s1 and s2s2 are the distances from each slit to the point.
What is ΔsΔs (in nm) at Point P?
What is ΔsΔs (in nm) at Point Q?
What is ΔsΔs (in nm) at Point R?
The interference figure of a set of double slits is measured on a screen. The experiment is carried out with a laser with a wavelength of 450 nm (approach the speed of light to 300,000 km/s in this situation) and it is measured that the interference maximum m=2 is 10 mm away from the main maximum. Then 2 pieces of glass are placed in front of each of the slits. The piece of glass P1 causes a delay in the wave (relative to a wave traveling in air) of 7.5 10^(-16) s. The piece of glass P2 causes a delay of 3.75 10^(-16) s. How many mm will the main maximum be shifted from the initial position?
In a Young's double-slit experiment, the separation between slits is d and
the screen is a distance R from the slits. R is much greater than d and > is
the wavelength of the light. The number of bright fringes per unit width
on the screen is:
d/RX
R/dλ
Rd/λ
X/Rd
Rλ/d
Chapter 27 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 27.3 - Which of the following causes the fringes in a...Ch. 27.5 - In a laboratory accident, you spill two liquids...Ch. 27.5 - Prob. 27.3QQCh. 27.6 - Prob. 27.4QQCh. 27.7 - Suppose you are observing a binary star with a...Ch. 27.8 - Ultraviolet light of wavelength 350 nm is incident...Ch. 27 - Consider a wave passing through a single slit....Ch. 27 - Prob. 2OQCh. 27 - Suppose Youngs double-slit experiment is performed...Ch. 27 - Prob. 4OQ
Ch. 27 - Prob. 5OQCh. 27 - Prob. 6OQCh. 27 - A monochromatic beam of light of wavelength 500 nm...Ch. 27 - A film of oil on a puddle in a parking lot shows a...Ch. 27 - Prob. 9OQCh. 27 - A Fraunhofer diffraction pattern is produced on a...Ch. 27 - Prob. 11OQCh. 27 - Prob. 12OQCh. 27 - Why is it advantageous to use a large-diameter...Ch. 27 - Prob. 1CQCh. 27 - Prob. 2CQCh. 27 - Prob. 3CQCh. 27 - Prob. 4CQCh. 27 - Why is the lens on a good-quality camera coated...Ch. 27 - Prob. 6CQCh. 27 - Prob. 7CQCh. 27 - Prob. 8CQCh. 27 - A laser beam is incident at a shallow angle on a...Ch. 27 - Prob. 10CQCh. 27 - Prob. 11CQCh. 27 - Prob. 12CQCh. 27 - John William Strutt, Lord Rayleigh (1842–1919),...Ch. 27 - Prob. 1PCh. 27 - Youngs double-slit experiment underlies the...Ch. 27 - Two radio antennas separated by d = 300 m as shown...Ch. 27 - Prob. 4PCh. 27 - Prob. 5PCh. 27 - Prob. 6PCh. 27 - In Figure P27.7 (not to scale), let L = 1.20 m and...Ch. 27 - Prob. 8PCh. 27 - Prob. 9PCh. 27 - Prob. 10PCh. 27 - Two slits are separated by 0.180 mm. An...Ch. 27 - Prob. 12PCh. 27 - A pair of narrow, parallel slits separated by...Ch. 27 - Coherent light rays of wavelength strike a pair...Ch. 27 - Prob. 15PCh. 27 - Prob. 16PCh. 27 - A riverside warehouse has several small doors...Ch. 27 - Prob. 18PCh. 27 - Prob. 19PCh. 27 - Astronomers observe the chromosphere of the Sun...Ch. 27 - Prob. 21PCh. 27 - Prob. 22PCh. 27 - A beam of 580-nm light passes through two closely...Ch. 27 - Prob. 24PCh. 27 - An air wedge is formed between two glass plates...Ch. 27 - Prob. 26PCh. 27 - Prob. 27PCh. 27 - Prob. 28PCh. 27 - Prob. 29PCh. 27 - Prob. 30PCh. 27 - Prob. 31PCh. 27 - Prob. 32PCh. 27 - A beam of monochromatic green light is diffracted...Ch. 27 - Prob. 34PCh. 27 - Prob. 35PCh. 27 - Prob. 36PCh. 27 - Prob. 37PCh. 27 - Prob. 38PCh. 27 - Prob. 39PCh. 27 - White light is spread out into its spectral...Ch. 27 - Prob. 41PCh. 27 - Prob. 42PCh. 27 - Prob. 43PCh. 27 - Prob. 44PCh. 27 - Prob. 45PCh. 27 - Prob. 46PCh. 27 - Prob. 47PCh. 27 - Prob. 48PCh. 27 - Prob. 49PCh. 27 - Prob. 50PCh. 27 - Prob. 51PCh. 27 - A wide beam of laser light with a wavelength of...Ch. 27 - Prob. 53PCh. 27 - Prob. 54PCh. 27 - Prob. 55PCh. 27 - Prob. 56PCh. 27 - Prob. 57PCh. 27 - Prob. 58PCh. 27 - Prob. 59PCh. 27 - Prob. 60PCh. 27 - Prob. 61PCh. 27 - Prob. 62PCh. 27 - Both sides of a uniform film that has index of...Ch. 27 - Prob. 64PCh. 27 - Light of wavelength 500 nm is incident normally on...Ch. 27 - Prob. 66PCh. 27 - A beam of bright red light of wavelength 654 nm...Ch. 27 - Iridescent peacock feathers are shown in Figure...Ch. 27 - Prob. 69PCh. 27 - Prob. 70PCh. 27 - Figure CQ27.4 shows an unbroken soap film in a...
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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_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
- Coherent 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 P36.9. 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. Figure P36.9arrow_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_forwardIn a 2-slit experiment, one of the slits is covered by a thin film of refractive index n1 and the other slit is covered by another thin film of refractive index n2 (n1>n2). Both films have the same thickness t. A flat screen is located a distance L from the slits. The slit spacing is d. Find the shift in the position of the central maximum of the interference pattern because of the presence of the thin films.arrow_forward
- A two-slit Young’s interference experiment is arranged with the wavelength of the light source λ = 0.5 μm. When a thin film of transparent material is put in front of one of the slits, the zero order fringe moves to the position previously occupied by the 4th order bright fringe. The index of refraction of the film is n = 1.2. Calculate the thickness of the film.arrow_forwardThe interference figure of a set of double slits is measured at a stop. The experiment is performed with a laser with a wavelength of 450nm (approach the speed of light to 300,000 km/s in this situation) and it is measured that the interference maximum m=2 is 10mm away from the main maximum.Then, 2 pieces of glass are placed in front of each of the slits. The piece of glass P1 causes a delay in the wave (in relation to a wave that propagates in the air) of 7.5x10^(-16)sThe piece of P2 glass causes a delay of 3.75x10^(-16)s. How many mm will the main maximum be shifted from the initial position?a)1.25 towards P1b)1.25 towards P2c)1.50 towards P1d)1.50 towards P2e)1.75 towards P1f)1.75 towards P2g)2.00 towards P1h)2.00 towards P2i)2.25 towards P1j)2.25 towards P2arrow_forwardA student performs a multiple-slit interference experiment. A coherent light source illuminates multiple slits in a barrier, and the resulting interference pattern is projected on a screen that is separated from the barrier by 2.2 m. The uniform spacing between the slits is 5.0μm5.0μm. A light sensor is used to measure the intensity of the light at the screen, and the student makes the following graph of the intensity as a function of the position along the screen as measured from the center of the central maximum. What is the wavelength, in nm, of the light source?arrow_forward
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