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physics
light and optics

Questions and Answers of Light and Optics

In Figure a broad beam of light of wavelength 683 nm is sent directly downward through the top plate of a pair of glass plates. The plates are 120 mm long, touch at the left end, and are separated by
In Figure a broad beam of light of wavelength 620 nm is sent directly downward through the top plate of a pair of glass plates touching at the left end. The air between the plate??s acts as a thin
In Figure two microscope slides touch at one end and are separated at the other end. When light of wavelength 500 nm shines vertically down on the slides, an overhead observer sees interference
In Figure a broad beam of monochromatic light is directed perpendicularly through two glass plates that are held together at one end to create a wedge of air between them. An observer intercepting
Figure a shows a lens with radius of curvature R lying on a flat glass plate and illuminated from above by light with wavelength ? Figure b, (a photograph taken from above the lens) shows that
In a Newton's rings experiment (see Problem 75), the radius of curvature R of the lens is 5.0 m and the lens diameter is 20 mm.(a) How many bright rings are produced? Assume that λ = 589 nm.(b) How
A Newton's rings apparatus is to be used to determine the radius of curvature of a lens. The radii of the nth and (n + 20)th bright rings are measured and found to be 0.1,62 and 0.368 cm,
A thin film of liquid is held in a horizontal circular ring, with air on both sides of the film. A beam of light at wavelength 550 nm is directed perpendicularly onto the film, and the intensity 1 of
If mirror Mz in a Michelson interferometer (Figure) is moved through 0.233mm, a shift of 792 bright fringes occurs. What is the wavelength of the light producing the fringepattern?
A thin film with index of refraction n = 1.40 is placed in one arm of a Michelson interferometer, perpendicular to the optical path. If this causes a shift of 7.0 bright fringes of the pattern
In Figure an airtight chamber of length d = 5.0 cm is placed in one of the arms of a Michelson interferometer. (The glass window on each end of the chamber has negligible thickness.) Light of
The element sodium can emit light at two wavelengths, λ1 = 589.10 nm and λ2 = 589.59 nm. Light from sodium is being used in a Michelson interferometer (Figure). Through what distance must mirror M2
Ocean waves moving at a speed of 4.0 m/s are approaching a beach at angle ?1 = 30o to the normal, as shown from above in Figure. Suppose the water depth changes abruptly at a certain distance from
Figure a, shows two light rays that are initially in phase as they travel upward through a block of plastic, with wavelength 400 nm as measured in air. Light ray r1 exits directly into air. However,
Two light rays, initially in phase and with a wavelength of 500 nm, go through different paths by reflecting from the various mirrors shown in Figure. (Such a reflection does not itself produce a
In Figure two isotropic point sources S1 and S2 emit light in phase at wavelength 1 and at the same amplitude. The sources are separated by distance d = 6.00? on an x axis. A viewing screen is at
In Figure a microwave transmitter at height a above the water level of a wide lake transmits microwaves of wavelength ? toward a receiver on the opposite shore, a distance x above the water level.
In Figure two isotropic point sources S1 and S2 emit light at wavelength ? = 400 nm. Source S1 is located at y = 640 nm; source S2 is located at y = ?? 640 nm. At point P1 (at x = 120 nm), the wave
A double-slit arrangement produces bright interference fringes for sodium light (λ = 589 nm) that are angularly separated by 0.30o near the center of the pattern. What is the angular fringe
Two light rays, initially in phase and with a wavelength of 500 nm, go through different paths by reflecting from the various mirrors shown in Figure. (Such a reflection does not itself produce a
In a phasor diagram for the waves at any point on the viewing screen for the two-slit experiment in Figure the phasor of the resultant wave rotates 60.0o in 2.50 x 10-16 s. What is the wavelength of
Light of wavelength 700.0 nm is sent along a route of length 2000 nm. The route is then filled with a medium having an index of refraction of 1.400. In degrees, by how much does the medium
Two parallel slits are illuminated with monochromatic light of wavelength 500 nm. An interference pattern is formed on a screen some distance from the slits, and the fourth dark band is located 1.68
In two experiments, light is to be sent along the two paths shown in Figure by reflecting it from the various flat surfaces shown. In the first experiment, rays 1 and 2 are initially in phase and
Find the slit separation of a double-slit arrangement that will produce interference fringes 0.018 rad apart on a distant screen when the light has wavelength λ = 589 nm.
A thin film suspended in air is 0.410μm thick and is illuminated with white light incident perpendicularly on its surface. The index of refraction of the film is 1.50. At what wavelength wills
In Figure a, the waves along rays 1 and 2 are initially in phase, with the same wavelength ? in air. ?Ray 2 goes through a material with length L and index of refraction n. The rays are then
A 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 i that
If the distance between the first and tenth minima of a double-slit pattern is 18.0 mm and the slits are separated by 0.150 mm with the screen 50.0 cm from the slits, what is the wavelength of the
What is the speed in fused quartz of light of wavelength 550 nm? (SeeFigure)
In Sample Problem assume that the coating eliminates the reflection of light of wavelength 550 nm at normal incidence. By what percentages is reflection diminished by the coating at (a) 450 nm and
Laser light of wavelength 632.8 nm passes through a double-slit arrangement at the front of a lecture room, reflects off a mirror 20.0 m away at the back of the room, and then produces an
Light of wavelength λ is used in a Michelson interferometer. Let x be the position of the movable mirror, with x = 0 when the arms have equal lengths d2 = d1. Write an expression for the
A sheet of glass having an index of refraction of 1.40 is to be coated with a film of material having an index of refraction of 1.55 in order that green light with a wavelength of 525nm (in air) will
One slit of a double-slit arrangement is covered by a thin glass plate with index of refraction 1.4 and the other by u thin glass plate with index of refraction 1.7. The point on the screen at which
In Figure two glass plates are held together at one end to form a wedge of air that acts as a thin film. A broad beam of light of wavelength 480 nm is directed through the plates, perpendicular to
A broad beam of light of wavelength 600 nm is sent directly downward through the glass plate (n = 1.50) in Figure. That plate and a plastic plate (n = 1.20) form a thin wedge of air that acts as a
Sodium light (λ = 589 nm) illuminates two slits separated by d = 2.0 mm. The slit-screen distance D is 40 mm. What percentage error is made by using Eq. 35-14 to locate the m : 10 bright fringe on
Figure shows an optical fiber in which a central plastic core of index of refraction n1 = 1.58 is surrounded by a plastic sheath of index of refraction n2 = 1.53. Light can travel along different
When an electron moves through a medium at a speed exceeding the speed of light in that medium, the electron radiates electromagnetic energy (the Cerenkov effect). What minimum speed must an electron
Point sources S1 and S2 radiate in phase at wavelength 400 nm and at the same amplitude. The sources are located on an x axis at x = 6.5μm and x = – 6.0μm, respectively. (a) Determine
The second dark band in a double-slit interference pattern is I.2 cm from the central maximum of the pattern. The separation between the two slits is equal to 800 wavelengths of the monochromatic
In Figure two glass plates (n = 1.60) form a wedge, and a fluid (n = 1.50) fills the wedge-shaped space. At the left end the plates touch; at the right, they are separated by 580 nm. Light with a
A thin film (n = 1.25) is deposited on a glass plate (n = 1.40) and illuminated with light of wavelength 550nm (measured in air). The light beam is perpendicular to the plate.What is the minimum
A light beam with a wavelength of 600 nm in air passes through film 1 (n1 = 1.2) of thickness 1.0μm, then through film 2 (air) of thickness 1.5 pm, and finally through film 3 (n3 = 1.8) of
Two light rays, initially in phase and having wavelength λ = 6.00 x 10-7 rn, pass through different plastic layers of the same thickness, 7.00 x 10-6 m. The indexes of refraction are 1.65 for
In a double-slit interference experiment, the slit separation is 2.00μm, the light wavelength is 500 nm, and the separation between the slits and the screen is 4.00 m. (a) What is the angle
A plane monochromatic light wave in air is perpendicularly incident on a thin film of oil that covers a glass plate. The wavelength of the source may be varied continuously. Fully destructive
Figure shows the design of a Texas arcade game. Four laser pistols are pointed toward the center of an array of plastic layers where a clay armadillo is the target. The indexes of refraction of the
In Figure let the angle θ of the two rays be 20.0o, slit separation d be 58.00μm, and wavelength λ be 500.9 nm. (a) What multiple of λ gives the phase difference of the two rays
Slits of unequal widths are used in a double-slit arrangement to produce an interference pattern on a distant screen. If only the narrower slit I is illuminated (the wider slit 2 is covered), the
Figure shows two point sources, S1 and S2 that emit light at wavelength λ = 500 nm and with the same amplitude. The emissions are isotropic and in phase, and the separation between the sources ts d
(a) Use the result of Problem to show that, in a Newton's rings experiment, the difference in radius between adjacent bright rings (maxima) is given by Δr = r m+1 – rm ≈ ½
A single slit is illuminated by light of wavelengths λa and λb chosen so that the first diffraction minimum of the λab component coincides with the second minimum of the λb component.(a) If λb =
Monochromatic light of wavelength 441 nm is incident on a narrow slit. On a screen 2.00 m away, the distance between the second diffraction minimum and the central maximum is 1.50 cm.(a) Calculate
Light of wavelength 633 nm is incident on a narrow slit. The angle between the first diffraction minimum on one side of the central maximum and the first minimum on the other side is 1.20o. What is
What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at θ = 45.0o?
A plane wave of wavelength 590 nm is incident on a slit with a width of a = 0.40 mm. A thin converging lens of focal length +70 cm is placed between the slit and a viewing screen and focuses the
In conventional television, signals are broadcast from towers to home receivers. Even when a receiver is not in direct view of a tower because of a hill or building, it can still intercept a signal
The distance between the first and fifth minima of a single-slit diffraction pattern is 0.35 mm with the screen 40 cm away from the slit, when light of wavelength 550 nm is used.(a) Find the slit
Manufacturers of wire (and other objects of small dimension) sometimes use a laser to continually monitor the thickness of the product. The wire intercepts the laser beam, producing a diffraction
A slit 1.00 mm wide is illuminated by light of wavelength 589 nm. We see a diffraction pattern on a screen 3.00 m away. What is the distance between the first two diffraction minima on the same side
Sound waves with frequency 3000 Hz and speed 343 m/s diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length d = 100 m. The opening, which has a horizontal
Monochromatic light with wavelength 538 nm is incident on a slit with width 0.025 mm. The distance from the slit to a screen is 3.5m. Consider a point on the screen 1.1 cm from the central maximum.
(a) What is the ratio of Ip to the intensity Im at the center of the pattern?(b) Determine where point P is in the diffraction pattern by giving the maximum and minimum between which it lies, or the
A 0.10-mm-wide slit is illuminated by light of wavelength 589 nm. Consider a point P on a viewing screen on which the diffraction pattern of the slit is viewed; the point is at 30o from the central
Figure gives a versus the sine of the angle θ in a single-slit diffraction experiment using light of wavelength 610 nm. The vertical axis scale is set by as = 12 rad. What are? (a) The slit
(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating Eq. 36-5 with respect to a and equating the result to zero, obtaining
Babinet's principle, a monochromatic beam of parallel light is incident on a "collimating" hole of diameter x >> A. Point P lies in the geometrical shadow region on a distant screen (Figure a)
The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the
The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as 85 cm across (see Google Earth), and the telescopes on military surveillance satellites
If Superman really had x-ray vision at 0.10 nm wavelength and a 4.0 mm pupil diameter, at what maximum altitude could he distinguish villains from heroes, assuming that he needs to resolve points
Assume that Rayleigh's criterion gives the limit of resolution of an astronaut's eye looking down on Earth's surface from a typical space shuttle altitude of 400 km. (a) Under that that idealized
The two headlights of an approaching automobile are 1.4 m apart. At what(a) Angular separation and(b) Maximum distance wills the eye resolve them? Assume that the pupil diameter is 5.0 mm, and use a
Entopic halos if someone looks at a bright outdoor lamp in otherwise dark surroundings, the lamp appears to be surrounded by bright and dark rings (hence halos) that are actually a circular
Find the separation of two points on the Moon's surface that can just be resolved by the 200 in. (= 5.1 m) telescope at Mount Palomar, assuming that this separation is determined by diffraction
The radar system of a navy cruiser transmits at a wavelength of 1.6 cm, from a circular antenna with a diameter of 2.3 m. At a range of 6.2 km, what is the smallest distance that two speedboats can
Estimate the linear separation of two objects on Mars that can just be resolved under ideal conditions by an observer on Earth(a) Using the naked eye and(b) Using the 200 in. (= 5.1m) Mount Palomar
The wall of a large room is covered with acoustic tile in which small holes are drilled 5.0 mm from center to center. How far can a person be from such a tile and still distinguish the individual
(a) How far from grains of red sand must you be to position yourself just at the limit of resolving the grains if your pupil diameter is 1.5 mm, the grains are spherical with radius 50 pm, and the
Floaters the floaters you see when viewing a bright, featureless background are diffraction patterns of defects in the vitreous humor that fills most of your eye. Sighting through a pinhole sharpens
Millimeter-wave radar generates a narrower beam than conventional microwave radar, making it less vulnerable to antiradar missiles than conventional radar.(a) Calculate the angular width 20 of the
(a) A circular diaphragm 60 cm in diameter oscillates at a frequency of 25 kHz as an underwater source of sound used for submarine detection. Far from the source, the sound intensity is distributed
Nuclear-pumped x-ray lasers ate seen as a possible weapon to destroy ICBM booster rockets at ranges up to 2000 km. One limitation on such a device is the spreading of the beam due to diffraction,
The wings of tiger beetles (Figure) are colored by interference due to thin cuticle-like layers. In addition, these layers are arranged in patches that are 60μm across and produce different colors.
(a) What is the angular separation of two stars if their images are barely resolved by the Thaw refracting telescope at the Allegheny Observatory in Pittsburgh? The lens diameter is 76 cm and its
A circular obstacle produces the same diffraction pattern as a circular hole of the same diameter (except very near 6 = 0). Airborne water drops are examples of such obstacles. When you see the Moon
In a double-slit experiment, the slit separation d is 2.00 times the slit width w. How many bright interference fringes are in the central diffraction envelope?
A beam of light of a single wavelength is incident perpendicularly on a double-slit arrangement, as in Figure. The slit widths are each 46μm and the slit separation is 0.30 mm. How many complete
Suppose that the central diffraction envelope of a double-slit diffraction pattern contains 11 bright fringes and the first diffraction minima eliminate (are coincident with) bright fringes. How many
Two slits of width a and separation d are illuminated by a coherent beam of light of wavelength λ. What is the linear separation of the bright interference fringes observed on a screen that is at a
(a) How many bright fringes appear between the first diffraction-envelope minima to either side of the central maximum in a double-slit pattern if λ = 550 nm, d = 0.150nm, and a = 30.0μm?(b) What
(a) In a double-slit experiment, what ratio of d to a causes diffraction to eliminate the fourth bright side fringe?(b) What other bright fringes are also eliminated?
Light of wavelength 440 nm passes through a double slit, yielding a diffraction pattern whose graph of intensity l versus angular position θ is shown in Figure calculate (a) The slit width and (b)
Figure gives the parameter B of Eq. 36-20 versus the sine of the angle θ in a two-slit interference experiment using light of wavelength 435nm. The vertical axis scale is set by βs = 80.0 rad what
(a) What is the ratio of Ip to the intensity Im at the center of the pattern?(b) Determine where P is in the two-slit interference pattern by giving the maximum or minimum on which it lies or the
Visible light is incident perpendicularly on a grating with 315rulings/mm. What is the longest wavelength that can be seen in the fifth-order diffraction?
A grating has 400lines/mm. How many orders of the entire visible spectrum (400-700 nm) can it produce in a diffraction experiment, in addition to the m = 0 order?
Perhaps to confuse a predator, some tropical gyrinid beetles (whirligig beetles) are colored by optical interference that is due to scales whose alignment forms a diffraction grating (which scatters
A diffraction grating 20.0 mm wide has 6000 rulings. Light of wavelength 589 nm is incident perpendicularly on the grating. What are the(a) Largest,(b) Second largest, and(c) Third largest values of

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