17th Edition

ISBN: 9781938168185

Author: William Moebs, Jeff Sanny

Publisher: OpenStax

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The word "constructive" signifies addition in interference. Constructive interference occurs when the path of the waves that start from the slit differs by 1 entire wavelength or in the intervals of the same. Hence, the waves that are presented on the sc…

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Chapter 4, Problem 100AP

Two lamps producing light of wavelength 589 nm are fixed 1.0 m apart on a wooden plank. What is the maximum distance an observer can be and still resolve the lamps as two separate sources of light, if the resolution is affected solely by the diffraction of light entering the eye? Assume light enters the eye through a pupil of diameter 4.5 mm.

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Chapter 4, Problem 99AP

Chapter 4, Problem 101AP

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The limit to the eye’s visual acuity is related to diffraction by the pupil.Randomized VariablesD = 3.05 mmdh = 1.4 m Part (a) What is the angle between two just-resolvable points of light for a 3.05 mm diameter pupil in radians, assuming an average wavelength of 550 nm? Part (b) Take your result to be the practical limit for the eye. What is the greatest possible distance in km a car can be from you if you can resolve its two headlights, given they are 1.4 m apart? Part (c) What is the distance between two just-resolvable points held at an arm’s length (0.800 m) from your eye in mm?

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The maximum resolution of the eye depends on the diameter of the opening of the pupil (a diffraction effect) and the size of the retinal cells. The size of the retinal cells (about 5.0 mm in diameter) limits the size of an object at the near point (25 cm) of the eye to a height of about 50 µm. (To get a reasonable estimate without having to go through complicated calculations, we shall ignore the effect of the fluid in the eye.) (a) Given that the diameter of the human pupil is about 2.0 mm, does the Rayleigh criterion allow us to resolve a 50 -µm -tall object at 25 cm from the eye with light of wavelength 550 nm? (b) According to the Rayleigh criterion, what is the shortest object we could resolve at the 25 cm near point with light of wavelength 550 nm? (c) What angle would the object in part (b) subtend at the eye? Express your answer in minutes 160 min = 1°2, and compare it with the experimental value of about 1 min. (d) Which effect is more important in limiting the resolution of…

Chapter 4 Solutions

University Physics Volume 3

Ch. 4 - Check Your Understanding Suppose the slit width in...Ch. 4 - Check Your Understanding For the experiment in...Ch. 4 - Check Your Understanding For the experiment in...Ch. 4 - Check Your Understanding If the line spacing of a...Ch. 4 - Check Your Understanding What is the angular...Ch. 4 - Check Your Understanding For the experiment...Ch. 4 - As the width of the slit producing a single-slit...Ch. 4 - Compare interference and diffraction.Ch. 4 - If you and a friend are on opposite sides of a...Ch. 4 - What happens to the diffraction pattern of a...

Ch. 4 - In our study of diffraction by a single slit, we...Ch. 4 - A rectangular slit is twice as wide as it is high....Ch. 4 - In Equation 4.4, the parameter looks like an...Ch. 4 - Shown below is the central part of the...Ch. 4 - Is higher resolution obtained in a microscope with...Ch. 4 - The resolving power of refracting telescope...Ch. 4 - The distance between atoms in a molecule is about...Ch. 4 - A beam of light always spreads out. Why can a beam...Ch. 4 - Crystal lattices can be examined with X-rays but...Ch. 4 - How can you tell that a hologram is a true...Ch. 4 - If a hologram is recorded using monochromatic...Ch. 4 - What image will one see if a hologram is recorded...Ch. 4 - (a) At what angle is the first minimum for 550-nm...Ch. 4 - (a) Calculate the angle at which a 2.00-m-wide...Ch. 4 - (a) How wide is a single slit that produces its...Ch. 4 - (a) What is the width of a single slit that...Ch. 4 - Find the wavelength of light that has its third...Ch. 4 - (a) Sodium vapor light averaging 589 nm in...Ch. 4 - Consider a single-slit diffraction pattern for...Ch. 4 - (a) Find the angle between the first minima for...Ch. 4 - What is the minimum width of a single slit (in...Ch. 4 - (a) If a single slit produces a first minimum at...Ch. 4 - If the separation between the first and the second...Ch. 4 - A water break at the entrance to a harbor consists...Ch. 4 - An aircraft maintenance technician walks past a...Ch. 4 - A single slit of width 3.0 m is illuminated by a...Ch. 4 - A single slit of width 0.1 mm is illuminated by a...Ch. 4 - The width of the central peak in a single-slit...Ch. 4 - Consider the single-slit diffraction pattern for...Ch. 4 - Two slits of width 2 m, each in an opaque...Ch. 4 - A double slit produces a diffraction pattern that...Ch. 4 - For a double-slit configuration where the slit...Ch. 4 - Light of wavelength 500 nm falls normally on 50...Ch. 4 - A monochromatic light of wavelength 589 nm...Ch. 4 - When a monochromatic light of wavelength 430 nm...Ch. 4 - Determine the intensities of two interference...Ch. 4 - A diffraction grating has 2000 lines per...Ch. 4 - Find the angle for the third-order maximum for...Ch. 4 - How many lines per centimeter are there on a...Ch. 4 - What is the distance between lines on a...Ch. 4 - Calculate the wavelength of light that has its...Ch. 4 - An electric current through hydrogen gas produces...Ch. 4 - (a) What do the four angles in the preceding...Ch. 4 - What is the spacing between structures in a...Ch. 4 - An opal such as that shown in Figure 4.15 acts...Ch. 4 - At what angle does a diffraction grating produce a...Ch. 4 - (a) Find the maximum number of lines per...Ch. 4 - (a) Show that a 30,000 line per centimeter grating...Ch. 4 - The analysis shown below also applies to...Ch. 4 - The 305-m-diameter Arecibo radio telescope...Ch. 4 - Assuming the angular resolution found for the...Ch. 4 - Diffraction spreading for a flashlight is...Ch. 4 - (a) What is the minimum angular spread of a 633-nm...Ch. 4 - A telescope can be used to enlarge the diameter of...Ch. 4 - The limit to the eye’s acuity is actually related...Ch. 4 - What is the minimum diameter mirror on a telescope...Ch. 4 - Find the radius of a star’s image on the retina of...Ch. 4 - (a) The dwarf planet Pluto and its moon, Charon,...Ch. 4 - A spy satellite orbits Earth at a height of 180...Ch. 4 - What is the minimum angular separation of two...Ch. 4 - The headlights of a car are 1.3 m apart. What is...Ch. 4 - When dots are placed on a page from a laser...Ch. 4 - Suppose you are looking down at a highway from a...Ch. 4 - Can an astronaut orbiting Earth in a satellite at...Ch. 4 - The characters of a stadium scoreboard are formed...Ch. 4 - If a microscope can accept light from objects at...Ch. 4 - A camera uses a lens with aperture 2.0 cm. What is...Ch. 4 - X-rays of wavelength 0.103 nm reflects off a...Ch. 4 - A first-order Bragg reflection maximum is observed...Ch. 4 - An X-ray scattering experiment is performed on a...Ch. 4 - The structure of the NaCl crystal forms reflecting...Ch. 4 - On a certain crystal, a first-order X-ray...Ch. 4 - Calcite crystals contain scattering planes...Ch. 4 - The first-order Bragg angle for a certain crystal...Ch. 4 - White light falls on two narrow slits separated by...Ch. 4 - Microwaves of wavelength 10.0 mm fall normally on...Ch. 4 - Quasars, or quasi-stellar radio sources, are...Ch. 4 - Two slits each of width 1800 nm and separated by...Ch. 4 - A microwave of an unknown wavelength is incident...Ch. 4 - Red light (wavelength 632.8 nm in air) from a...Ch. 4 - A light ray of wavelength 461.9 nm emerges from a...Ch. 4 - How far apart must two objects be on the moon to...Ch. 4 - How far apart must two objects be on the moon to...Ch. 4 - A spy satellite is reputed to be able to resolve...Ch. 4 - Monochromatic light of wavelength 530 nm passes...Ch. 4 - A monochromatic light of unknown wavelength is...Ch. 4 - A source of light having two wavelengths 550 nm...Ch. 4 - A single slit of width 2100 nm is illuminated...Ch. 4 - A single slit of width 3.0 m is illuminated by a...Ch. 4 - A single slit of width 0.10 mm is illuminated by a...Ch. 4 - A diffraction grating produces a second maximum...Ch. 4 - A grating with 4000 lines per centimeter is used...Ch. 4 - A diffraction grating with 2000 lines per...Ch. 4 - For white light (400nm700nm) falling normally on a...Ch. 4 - How many complete orders of the visible spectrum...Ch. 4 - Two lamps producing light of wavelength 589 nm are...Ch. 4 - On a bright clear day, you are at the top of a...Ch. 4 - Radio telescopes are telescopes used for the...Ch. 4 - Calculate the wavelength of light that produces...Ch. 4 - (a) Find the angle of the third diffraction...Ch. 4 - As an example of diffraction by apertures of...Ch. 4 - What are the angular positions of the first and...Ch. 4 - How far would you place a screen from the slit of...Ch. 4 - How narrow is a slit that produces a diffraction...Ch. 4 - Suppose that the central peak of a single-slit...Ch. 4 - The central diffraction peak of the double-slit...Ch. 4 - Determine the intensities of three interference...Ch. 4 - The yellow light from a sodium vapor lamp seems to...Ch. 4 - Structures on a bird feather act like a reflection...Ch. 4 - If a diffraction grating produces a first-order...Ch. 4 - (a) What visible wavelength has its fourth-order...Ch. 4 - Consider a spectrometer based on a diffraction...Ch. 4 - An amateur astronomer wants to build a telescope...Ch. 4 - Blue light of wavelength 450 nm falls on a slit of...Ch. 4 - (a) Assume that the maxima are halfway between the...Ch. 4 - (a) By differentiating Equation 4.4, show that the...Ch. 4 - What is the maximum number of lines per centimeter...Ch. 4 - Show that a diffraction grating cannot produce a...Ch. 4 - A He-Ne laser beam is reflected from the surface...Ch. 4 - Objects viewed through a microscope are placed...

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