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, Problem 43AP
(a)
To determine
To show: The condition of sharp view for monochromatic light with plane wave fronts
(b)
To determine
The optimum pinhole diameter for
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A pinhole camera has a small circular aperture of diameter D. Light from distant objects passes through the aperture into an otherwise dark box, falling on a screen located a distance L away. If D is too large, the display on the screen will be fuzzy because a bright point in the field of view will send light onto a circle of diameter slightly larger than D. On the other hand, if D is too small, diffraction will blur the display on the screen. The screen shows a reasonably sharp image if the diameter of the central disk of the diffraction pattern, specified by as shown, is equal to D at the screen. (a) Show that for monochromatic light with plane wave fronts and L >> D, the condition for a sharp view is fulfilled if D2 = 2.44λL. (b) Find the optimum pinhole diameter for 500-nm light projected onto a screen 15.0 cm away.
One way to determine the index of refraction of a gas is to use an interferometer. As shown below, one of the beams of an interferometer passes through a glass container that has a length of L = 1.8 cm. Initially the glass container is a vacuum. When gas is slowly allowed into the container, a total of 6894 dark fringes move past the reference line. The laser has a wavelength of 635 nm (this is the wavelength when the light from the laser is moving through a vacuum).
A.) Determine how many wavelengths will fit into the glass container when it is a vacuum. Since the light passes through the container twice, you need to determine how many wavelengths will fit into a glass container that has a length of 2L.number of wavelengths (vacuum) =
B.) The number of dark fringes is the difference between the number of wavelengths that fit in the container (length of 2L) when it has gas and the number of wavelengths that fit in the container (length of 2L) when it is a vacuum. Use this knowledge to…
In a double-slit experiment, the optical
path difference between the rays from two
coherent sources at a point P on one side of the
central bright band is 7.5 x 10 m and at a
point Q on the other side of the central bright
band is 1.8 x 10 m. How many bright and
dark bands are observed between points P and
Q if the wavelength of light used is 6 × 107 m?
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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- A beam of 580-nm light passes through two closely spaced glass plates at close to normal incidence as shown in Figure P27.23. For what minimum nonzero value of the plate separation d is the transmitted light bright?arrow_forwardA plano-convex lens has index of refraction n. The curved side of the lens has radius of curvature R and rests on a flat glass surface of the same index of refraction, with a film of index nflim between them, as shown in Figure P36.42. The lens is illuminated from above by light of wavelength . Show that the dark Newtons rings have radii given approximately by r=mRnfilm where r R and m is an integer. Figure P36.42arrow_forwardLight enters a prism of crown glass and refracts at an angle of 5.00 with respect to the normal at the interface. The crown glass has a mean index of refraction of 1.51. It is combined with one flint glass prism (n = 1.65) to produce no net deviation. a. Find the apex angle of the flint glass. b. Assume the index of refraction for violet light (v = 430 nm) is nv = 1.528 and the index of refraction for red light (r = 768 nm) is nr = 1.511 for crown glass. For flint glass using the same wavelengths, nv = 1.665 and nr = 1.645. Find the net dispersion.arrow_forward
- Figure CQ27.4 shows an unbroken soap film in a circular frame. The film thickness increases from top to bottom, slowly at first and then rapidly. As a simpler model, consider a soap film (n = 1.33) contained within a rectangular wire frame. The frame is held vertically so that the film drains downward and forms a wedge with flat faces. The thickness of the film at the top is essentially zero. The film is viewed in reflected white light with near-normal incidence, and the first violet ( = 420 nm) interference band is observed 3.00 cm from the top edge of the film. (a) Locate the first red ( = 680 nm) interference band. (b) Determine the film thickness at the positions of the violet and red bands. (c) What is the wedge angle of the film?arrow_forwardThe Rayleigh criterion provides a convenient way to describe the theoretical resolution (e.g. an ability to distinguish two bright objects ) of an optical system. The criterion states that two small bright sources of light can be resolved if the first diffraction minimum of the image of one source point just coincides with of further apart then the first maximum of another (see figure below). A converging lens, 37.7 mm in diameter, is used to form images of distant objects. Considering the diffraction by the lens, what angular separation must two distant point objects have in order to satisfy Rayleigh's criterion? Assume that the wavelength of the light from the distant objects is 439 nm. Provide your answer in millidegrees (mdeg).arrow_forwardA slit of width d is placed in front of a lens of focal length 0.5 m and is illuminated normally with light of wavelength 5.89 × 107 m. The first diffraction minima on either side of the central diffraction maximum are separated by 2 × 10-³ m. The width d of the slit is m.arrow_forward
- The Rayleigh criterion provides a convenient way to describe the theoretical resolution (e.g. an ability to distinguish two bright objects ) of an optical system. The criterion states that two small bright sources of light can be resolved if the first diffraction minimum of the image of one source point just coincides with of further apart then the first maximum of another (see figure below). A converging lens, 34.2 mm in diameter, is used to form images of distant objects. Considering the diffraction by the lens, what angular separation must two distant point objects have in order to satisfy Rayleigh's criterion? Assume that the wavelength of the light from the distant objects is 431 nm. Provide your answer in millidegrees (mdeg). Answer: Choose... +arrow_forwardA camera lens with index of refraction greater than 1.30 is coated with a thin transparent film of index of refraction 1.25 to eliminate by interference the reflection of light at wavelength l that is incident perpendicularly on the lens. What multiple of l gives the minimum film thickness needed?arrow_forwardA plano-convex lens with radius of curvature R = 3.2 m is in contact with a flat plate of glass. A light source and the observer's eye are both close to the normal, as shown in the figure below. The radius of the 51st bright Newton's ring is found to be 9.4 mm. What is the wavelength of the light produced by the source? nm 2//1 Need Help? Read It 8:36 PM 4/11/2021arrow_forward
- Parallel rays of green mercury light with a wavelength of 546 nm pass through a slit covering a convex lens with a focal length of 60 cm. In the focal plane of the lens, the distance from the central maximum to the first minimum is 10.2 mm. What must be the width of this slit?arrow_forwardOne way to determine the index of refraction of a gas is to use an interferometer. As shown below, one of the beams of an interferometer passes through a glass container that has a length of L = 1.8 cm. Initially the glass container is a vacuum. When gas is slowly allowed into the container, a total of 7571 dark fringes move past the reference line. The laser has a wavelength of 687 nm (this is the wavelength when the light from the laser is moving through a vacuum). Laser Mirror Glass Container Beam Splitter Diffraction Pattern Mirror A.) Determine how many wavelengths will fit into the glass container when it is a vacuum. Since the light passes through the container twice, you need to determine how many wavelengths will fit into a glass container that has a length of 2L. number of wavelengths (vacuum) = B.) The number of dark fringes is the difference between the number of wavelengths that fit in the container (length of 2L) when it has gas and the number of wavelengths that fit in…arrow_forwardIn a Newton's ring experiment the diameter of the 10th bright ring changes from 1.40cm to 1.27 cm as a liquid is introduced between the lens and the plate. Calculate the index of refraction of the liquid.arrow_forward
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