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essential university physics
Essential University Physics 3rd Edition Volume 2 Richard Wolfsonby - Solutions
X-ray diffraction in potassium chloride (KCl) results in a first-order maximum when 97-pm-wavelength X rays graze the crystal plane at 8.5°. Find the spacing between crystal planes.
In the second-order spectrum from a diffraction grating, yellow light at 588 nm overlaps violet light (wavelength range 390 nm– 450 nm) diffracted in a different order. What’s the exact wavelength of the violet light, and what’s the order of its diffraction?
NASA asks you to assess the feasibility of a single-mirror spacebased optical telescope that could resolve an Earth-size planet 5 light-years away. What do you conclude?
A thin film of toluene (n = 1.49) floats on water. Find the minimum film thickness if the most strongly reflected light has wavelength 460 nm.
What order is necessary to resolve 647.98-nm and 648.07-nm spectral lines using a 4500-line grating?
Find the total number of lines in a 2.5-cm-wide diffraction grating whose third-order spectrum puts the 656-nm hydrogen- α spectral line 37° from the central maximum.
For visible light with wavelengths from 400nm to 700 nm, show that the first-order spectrum is the only one that doesn’t overlap with the next higher order.
You’re designing a spectrometer whose specifications call for a minimum of 5° separation between the red hydrogen-α line at 656 nm and the yellow sodium line at 589 nm when the two are observed in third order with a grating spectrometer. Available gratings have 2500 lines/cm, 3500 lines/cm, or
On the screen of a multiple-slit system, the interference pattern shows bright maxima separated by 0.86° and seven minima between each bright maximum.(a) How many slits are there?(b) What’s the slit separation if the incident light has wavelength 656.3nm?
A tube of glowing gas emits light at 550 nm and 400 nm. In a double-slit apparatus, what’s the lowest-order 550-nm bright fringe that will fall on a 400-nm dark fringe, and what are the fringes’ corresponding orders?
A screen 1.0 m wide is 2.0m from a pair of slits illuminated by 633-nm laser light, with the screen’s center on the centerline of the slits. Find the highest-order bright fringe that will appear on the screen if the slit spacing is(a) 0.10mm(b) 10μm.
For a double-slit system with slit spacing 0.0525mm and wavelength 633 nm, at what angular position is the path difference a quarter wavelength?
A double-slit experiment has slit spacing 0.035 mm, slit-to screen distance 1.5m, and wavelength 490 nm. What’s the phase difference between two waves arriving at a point 0.56 cm from the center line of the screen?
Find the angular position of the second-order bright fringe in a double-slit system whose slit spacing is 1.5μm for(a) red light at 640 nm,(b) yellow light at 580 nm,(c) violet light at 410 nm.
In bright light, the human eye’s pupil diameter is about 2mm. If diffraction were the limiting factor, what’s the eye’s minimum angular resolution under these conditions, assuming 550-nm light?
What’s the longest wavelength of light you could use to resolve a structure with angular diameter 0.44 mrad, using a microscope with a 1.2-mm-diameter objective lens?
Find the minimum telescope aperture that could resolve an object with angular diameter 0.35 arcsecond, observed at 520-nm wavelength. (1 arcsec = 1/3600°.)
Find the minimum angular separation resolvable with 633-nm laser light passing through a circular aperture of diameter 2.1cm.
Find the intensity as a fraction of the central peak intensity for the second secondary maximum in single-slit diffraction, assuming the peak lies midway between the second and third minima.
You’re inside a metal building that blocks radio waves, but you’re trying to make a call with your cell phone, which broadcasts at a frequency of 950MHz. Down the hall from you is a narrow window measuring 35 cm wide. What’s the horizontal angular width of the beam (i.e., the angle between
Light with wavelength 633 nm is incident on a 2.50μm wide slit. Find the angular width of the central peak in the diffraction pattern, taken as the angular separation between the first minima.
For what ratio of slit width to wavelength will the first minima of a single-slit diffraction pattern occur at ±90°?
White light shines on a 75.0-nm-thick sliver of fluorite (n = 1.43). What wavelength is most strongly reflected?
Monochromatic light shines on a glass wedge with refractive index 1.65, and enhanced reflection occurs where the wedge is 450 nm thick. Find all possible values for the wavelength in the visible range.
Light of unknown wavelength shines on a precisely machined glass wedge with refractive index 1.52. The closest point to the apex of the wedge where reflection is enhanced occurs where the wedge is 98 nm thick. Find the wavelength.
Find the minimum thickness of a soap film (n = 1.333) in which 550-nm light will undergo constructive interference.
Light is incident normally on a grating with 10,000 lines/cm. Find the maximum order in which(a) 450-nm(b) 650-nm light will be visible.
Green light at 520nm is diffracted by a grating with 3000lines/cm. Through what angle is the light diffracted in(a) first(b) fifth order?
A five-slit system with 7.5μm slit spacing is illuminated with 633-nm light. Find the angular positions of(a) the first two maxima(b) the third and sixth minima.
In a three-slit system, the first minimum occurs at angular position 5°. Where is the next maximum?
In a five-slit system, how many minima lie between the zeroth-order and first-order maxima?
The 546-nm green line of gaseous mercury falls on a double-slit apparatus. If the fifth dark fringe is at 0.113° from the centerline, what’s the slit separation?
The interference pattern from two slits separated by 0.37mm has bright fringes with angular spacing 0.065°. Find the light’s wavelength.
A double-slit experiment has slit spacing 0.12 mm.(a) What should be the slit-to-screen distance L if the bright fringes are to be 5.0mm apart when the slits are illuminated with 633-nm laser light?(b) What will be the fringe spacing with 480-nm light?
A double-slit experiment with d = 0.025mm and L = 75 cm uses 550-nm light. Find the spacing between adjacent bright fringes.
A double-slit system is used to measure the wavelength of light. The system has slit spacing d = 15μm and slit-to-screen distance L = 2.2m. If the m = 1 maximum in the interference pattern occurs 7.1 cm from screen center, what’s the wavelength?
Sketch roughly the diffraction pattern you would expect for light passing through a square hole a few wavelengths wide.
The speed of a camera lens measures its ability to photograph in dim light. Speed is characterized by f-ratio, also called the f-number, defined as the ratio of focal length f to lens diameter d. Thus an f/2.8 lens, for example, has diameter d = f/2.8. The actual amount of light a lens admits
The speed of a camera lens measures its ability to photograph in dim light. Speed is characterized by f-ratio, also called the f-number, defined as the ratio of focal length f to lens diameter d. Thus an f/2.8 lens, for example, has diameter d = f/2.8. The actual amount of light a lens admits
The speed of a camera lens measures its ability to photograph in dim light. Speed is characterized by f-ratio, also called the f-number, defined as the ratio of focal length f to lens diameter d. Thus an f/2.8 lens, for example, has diameter d = f/2.8. The actual amount of light a lens admits
The speed of a camera lens measures its ability to photograph in dim light. Speed is characterized by f-ratio, also called the f-number, defined as the ratio of focal length f to lens diameter d. Thus an f/2.8 lens, for example, has diameter d = f/2.8. The actual amount of light a lens admits
A contact lens prescription calls for +2.25-diopter lenses with inner curvature radius 8.6mm to fit the patient’s cornea.(a) If the lenses are plastic with n = 1.56, what should be the outer curvature radius?(b) With these lenses, the patient comfortably reads a newspaper 30 cm from her eyes.
You stand with your nose 6.0 cm from the surface of a reflecting ball, and your nose’s image appears three-quarters full size. What’s the ball’s diameter?
To the unaided eye, Jupiter has an angular diameter of 50 arcseconds. What will its angular size be when viewed through a 1-m-focal-length refracting telescope with a 40-mm focal-length eyepiece?
A 300-power compound microscope has a 4.5-mm-focal-length objective lens. If the distance from objective to eyepiece is 10 cm, what should be the focal length of the eyepiece?
A camera can normally focus as close as 60 cm, but it has provisions for mounting additional lenses just in front of the main lens to provide close-up capability. What type and power of auxiliary lens will allow the camera to focus as close as 20 cm?
You’re taking a photography class, working with a camera whose zoom lens covers the focal-length range 38mm–110 mm. Your instructor asks you to compare the sizes of the images of a distant object when photographed at the two zoom extremes.
An object placed 17.5 cm from a convex lens of glass with n = 1.524 forms a virtual image twice the object’s size. If the lens is replaced with an identically shaped one made of diamond,(a) what type of image will appear (b) what will be its magnification?
A double-convex lens with equal 28.5-cm curvature radii is made from glass with refractive indices nred = 1.512 and nviolet = 1.547. If a point source of white light is located on the lens axis at 75.0 cm from the lens, over what distance will its visible image be smeared?
You’re an optician who’s been asked to design a new replacement lens for cataract patients. The lens must be 5.5mm in diameter, with focal length 17 mm, and it can’t be thicker than 0.8 mm. For the lens material, you have a choice of plastic with refractive index 1.49 or more expensive
An object is 28 cm from a double-convex lens with n = 1.5 and curvature radii 35 cm and 55 cm. Where is the image, and what type is it?
For what refractive index would the focal length of a planoconvex lens be equal to the curvature radius of its one curved surface?
A contact lens is in the shape of a convex meniscus (see Fig. 31.25). The inner surface is curved to fit the eye, with curvature radius 7.80mm. The lens is made from plastic with refractive index n = 1.56. If it has a 44.4-cm focal length, what?s the curvature radius of its outer surface? Plano-
Two specks of dirt are trapped in a crystal ball, one at the center and the other halfway to the surface. If you peer into the ball on a line joining the two specks, the outer one appears to be only onethird of the way to the other. Find the refractive index of the ball.
A slab of transparent material has thickness d and refractive index n that varies across the material: n(x) = n1 + (n2 - n1)(x/d2), where x is measured from one face of the slab. A light ray is incident normally on the slab. Find an expression for the time it takes to traverse the slab.
You’re an automotive engineer charged with evaluating safety glass, which is made by bonding a layer of flexible plastic between two layers of glass, thus eliminating dangerous glass fragments during accidents. A new product uses glass with refractive index n = 1.55 and plastic with n = 1.48.
Fermat’s principle states that a light ray’s path is such that the time to traverse that path is an extremum (a minimum or a maximum) when compared with times for nearby paths. Show that Fermat’s principle implies Snell’s law by proving that a light ray going from point A in one medium to
Show that a three-dimensional corner reflector (three mutually perpendicular mirrors, or a solid cube in which total internal reflection occurs) turns an incident light ray through 180°.
(a) Differentiate the result of Problem 55 to show that the maximum value of ϕ occurs when the incidence angle θ is given by cos2θ = 1/3 (n2 – 1).(b) Use this result and that of Problem 55 to find the maximum ϕ in a raindrop with n = 1.333. This is the angle at which
Figure 30.23 shows light passing through a spherical raindrop, undergoing two refractions and total internal reflection, resulting in an angle f between the incident and outgoing rays. Show that f = 4 sin-1 (sin ?/n) - 2?, where ? is the incidence angle. Incident ray B 180° - 4 Exiting ray FIGURE
Find an expression for the displacement x in Fig. 30.6, in terms of ?1, d, and n. に
You’re an optometrist, mounting a projector at the back of your 4.2-m-long exam room, 2.6 m above the floor. It shines an eyetest pattern on a white wall opposite the projector. Patients will sit with their eyes 3.3 m from the wall and 1.4m above the floor to view the pattern. At what height
Light is incident from air on the flat wall of a polystyrene water tank. If the incidence angle is 40°, what is the angle of refraction in the water?
For what diameter tank in Problem 50 will sunlight strike some part of the tank bottom whenever the Sun is above the horizon?Data From Problem 50A cylindrical tank 2.4m deep is full to the brim with water. Sunlight first hits part of the tank bottom when the rising Sun makes a 22° angle with the
A cylindrical tank 2.4m deep is full to the brim with water. Sunlight first hits part of the tank bottom when the rising Sun makes a 22° angle with the horizon. Find the tank’s diameter.
In a ruby laser, light is produced in a solid rod of ruby, with refractive index 1.77. The light emerges from the end of the rod into the surrounding air. At what angle should the rod end be cut so the emerging light is fully polarized?
In cataract surgery, ophthalmologists replace the eye’s natural lens with a synthetic intraocular lens, or IOL. A particular IOL has refractive index 1.452. Find the angle of refraction for a light ray striking this lens with incidence angle 77.0°. The medium before the IOL is the eye’s
White light propagating in air is incident at 45? on the equilateral prism of Fig. 30.19. Find the angular dispersion g of the outgoing beam if the prism has refractive indices nred = 1.582 and nviolet = 1.633. 45° Red Violet FIGURE 30.19 Exercise 27 (angles of dispersed rays aren't accurate)
Blue and red laser beams strike an air–glass interface with incidence angle 50°. If the glass has refractive indices of 1.680 for the blue light and 1.621 for the red, what will be the angle between the two beams in the glass?
Total internal reflection occurs at an interface between plastic and air at incidence angles greater than 37°. Find the plastic’s refractive index.
What is the critical angle for light propagating in glass with n = 1.52 when the glass is immersed in(a) water,(b) benzene,(c) diiodomethane?
The table below shows measurements of magnification versus object distance for a lens. Determine a quantity that, when you plot object distance against it, should give a straight line. Make your plot, establish a best-fit line, and use your line to find the focal length of the lens. Object
For visible wavelengths, the refractive index of the polycarbonate plastic widely used in eyeglasses is given approximately by n(λ) = b + c/ λ2, where b = 1.55 and c = 11,500 nm2 (a) Find an expression for the change in refractive index dn corresponding to a small wavelength change dλ.(b)
Chromatic aberration results from variation of the refractive index with wavelength. Starting with the lensmaker’s formula, find an expression for the fractional change df/f in the focal length of a thin lens in terms of the change dn in refractive index.
The maximum magnification of a simple magnifier occurs with the image at the 25-cm near point. Show that the angular magnification is m = 1 + (25 cm/f), where f is the focal length.
Galileo?s first telescope used the arrangement shown in Fig. 31.36, with a double-concave eyepiece slightly before the focus of the objective lens. Use ray tracing to show that this design gives an upright image, which makes the Galilean telescope useful in terrestrial observing. - fo- FIGURE
Draw a diagram like Fig. 31.10, but showing a ray from the arrowhead through the center of curvature. Using the fact that this ray reflects back on itself, draw similar triangles with object and image as their vertical sides, and show that the center of curvature is twice as far from the mirror as
Generalize the derivation of the lensmaker’s formula (Equation 31.7) to show that a lens of refractive index nlens in an external medium with index next has focal length given by ») = { - 1) (lensmaker's formula) (31.7) f
Show that identical objects placed equal distances on either side of the focal point of a concave mirror or converging lens produce images of equal size. Are the images of the same type?
Derive an expression for the thickness t of a plano-convex lens with diameter d, focal length f, and refractive index n.
Show that placing a 1-diopter lens in front of a 2-diopter lens gives the equivalent of a single 3-diopter lens (i.e., the powers of closely spaced lenses add).
Use Equation 31.6 to show that an object at the center of a glass sphere will appear to be its actual distance one radius from the edge. Draw a ray diagram showing why this makes sense. n2 n2 - n1 (31.6) s' R || ミ。
An object is 68 cm from a plano-convex lens whose curved side has curvature radius 26 cm. The refractive index of the lens is 1.62. Where is the image, and what type is it?
An object and its lens-produced real image are 2.4 m apart. If the lens has 55-cm focal length, what are the possible values for the object distance and magnification?
How far from a 25-cm-focal-length lens should you place an object to get an upright image magnified 1.8 times?
The cornea of the human eye has refractive index 1.38, while the eye’s lens has a graduated index in the range 1.38 to 1.40; use 1.39 for this problem. For the aqueous humor between cornea and lens, n = 1.34. Find the angle through which light is deflected at the first surface of(a) the cornea(b)
A candle and a screen are 70 cm apart. Find two points between candle and screen where you could put a convex lens with 17-cm focal length to give a sharp image of the candle on the screen.
How far apart are the object and image produced by a converging lens with 35-cm focal length when the object is(a) 40 cm(b) 30 cm from the lens
A lens has focal length f = 35 cm. Find the type and height of the image produced when a 2.2-cm-high object is placed at distances(a) f + 10 cm(b) f - 10 cm.
A converging lens has focal length 4.0 cm. A 1.0-cm-high arrow is located 7.0 cm from the lens with its lowest point 5.0mm above the lens axis. Make a full-scale ray-tracing diagram to locate both ends of the image. Confirm using the lens equation.
How far from a page should you hold a lens with 32-cm focal length in order to see the print magnified 1.6 times?
An object 15 cm from a concave mirror has a virtual image magnified 2.5 times. What’s the mirror’s focal length?
Find the polarizing angle for diamond when light is incident from air.
Light propagating in the glass 1n = 1.522 wall of an aquarium tank strikes the wall’s interior surface with incidence angle 12.4°. What’s the angle of refraction in the water?
A light ray propagates in a transparent material at 15° to the normal to the surface. It emerges into the surrounding air at 24° to the normal. Find the material’s refractive index.
Light is incident on an air–glass interface, and the refracted light in the glass makes a 40° angle with the normal to the interface. The glass has refractive index 1.52. Find the incidence angle.
Information in a compact disc is stored in “pits” whose depth is essentially one-fourth the wavelength of the laser light used to “read” the information. That wavelength is 780 nm in air, but the wavelength on which the pit depth is based is measured in the n = 1.55 plastic that makes up
At the aquarium where you work, a fish has gone missing in a 10-m-deep, 11-m-diameter cylindrical tank. You shine a flashlight in from the top edge of the tank, hoping to see if the missing fish is on the bottom. What’s the smallest angle your flashlight beam can make with the horizontal if
At what two distances could you place an object from a 45-cm-focal-length concave mirror to get an image 1.5 times the object’s size?
Viewed from Earth, the Moon subtends an angle of 0.52° in the sky. What will be the physical size of the Moon’s image formed by either of the twin Keck telescopes, with 10-m-diameter mirrors and 17.5-m focal length?
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