1 Million+ Step-by-step solutions

Helium–neon laser light (A = 632.8 nm) is sent through a 0.300-mm-wide single slit. What is the width of the central maximum on a screen 1.00 m from the slit?

A beam of green light is diffracted by a slit of width 0.550 mm. The diffraction pattern forms on a wall 2.06 m beyond the slit. The distance between the positions of zero intensity on both sides of the central bright fringe is 4.10 mm. Calculate the wavelength of the laser light.

A screen is placed 50.0 cm from a single slit, which is illuminated with 690-nm light. If the distance between the first and third minima in the diffraction pattern is 3.00 mm, what is the width of the slit?

Coherent microwaves of wavelength 5.00 cm enter a long, narrow window in a building otherwise essentially opaque to the microwaves. If the window is 36.0 cm wide, what is the distance from the central maximum to the first-order minimum along a wall 6.50 m from the window?

Sound with a frequency 650 Hz from a distant source passes through a doorway 1.10m wide in a sound-absorbing wall. Find the number and approximate directions of the diffraction-maximum beams radiated into the space beyond.

Light of wavelength 587.5 nm illuminates a single slit 0.750 mm in width.

(a) At what distance from the slit should a screen be located if the first minimum in the diffraction pattern is to be 0.850 mm from the center of the principal maximum?

(b) What is the width of the central maximum?

(a) At what distance from the slit should a screen be located if the first minimum in the diffraction pattern is to be 0.850 mm from the center of the principal maximum?

(b) What is the width of the central maximum?

A beam of laser light of wavelength 632.8 nm has a circular cross section 2.00 mm in diameter. A rectangular aperture is to be placed in the center of the beam so that, when the light falls perpendicularly on a wall 4.50 m away, the central maximum fills a rectangle 110 mm wide and 6.00 mm high. The dimensions are measured between the minima bracketing the central maximum. Find the required width and height of the aperture.

What If? Assume the light in Figure 38.5 strikes the single slit at an angle θ from the perpendicular direction. Show that Equation 38.1, the condition for destructive interference, must be modified to read

A diffraction pattern is formed on a screen 120 cm away from a 0.400-mm-wide slit. Monochromatic 546.1-nm light is used. Calculate the fractional intensity I / Imax at a point on the screen 4.10 mm from the center of the principal maximum.

Coherent light of wavelength 501.5 nm is sent through two parallel slits in a large flat wall. Each slit is 0.700 /m wide. Their centers are 2.80 /m apart. The light then falls on a semi cylindrical screen, with its axis at the midline between the slits.

(a) Predict the direction of each interference maximum on the screen, as an angle away from the bisector of the line joining the slits.

(b) Describe the pattern of light on the screen, specifying the number of bright fringes and the location of each.

(c) Find the intensity of light on the screen at the center of each bright fringe, expressed as a fraction of the light intensity Imax at the center of the pattern.

(a) Predict the direction of each interference maximum on the screen, as an angle away from the bisector of the line joining the slits.

(b) Describe the pattern of light on the screen, specifying the number of bright fringes and the location of each.

(c) Find the intensity of light on the screen at the center of each bright fringe, expressed as a fraction of the light intensity Imax at the center of the pattern.

The pupil of a cat’s eye narrows to a vertical slit of width 0.500 mm in daylight. What is the angular resolution for horizontally separated mice? Assume that the average wavelength of the light is 500 nm.

Find the radius a star image forms on the retina of the eye if the aperture diameter (the pupil) at night is 0.700 cm and the length of the eye is 3.00 cm. Assume the representative wavelength of starlight in the eye is 500 nm.

A helium–neon laser emits light that has a wavelength of 632.8 nm. The circular aperture through which the beam emerges has a diameter of 0.500 cm. Estimate the diameter of the beam 10.0 km from the laser.

You are vacationing in a Wonderland populated by friendly elves and a cannibalistic Cyclops that devours physics students. The elves and the Cyclops look precisely alike (everyone wears loose jeans and sweatshirts) except that each elf has two eyes, about 10.0 cm apart, and the Cyclops—you guessed it—has only one eye of about the same size as an elf’s. The elves and the Cyclops are constantly at war with each other, so they rarely sleep and all have red eyes, predominantly reflecting light with a wavelength of 660 nm. From what maximum distance can you distinguish between a friendly elf and the predatory Cyclops? The air in Wonderland is always clear. Dilated with fear, your pupils have a diameter of 7.00 mm.

If she is in a certain range of distances away, the viewer can resolve the separate tubes of one color but not the other. Which color is easier to resolve? The viewer’s distance must be in what range for her to resolve the tubes of only one color?

On the night of April 18, 1775, a signal was sent from the steeple of Old North Church in Boston to Paul Revere, who was 1.80 mi away: “One if by land, two if by sea.” At what minimum separation did the sexton have to set the lanterns for Revere to receive the correct message about the approaching British? Assume that the patriot’s pupils had a diameter of 4.00 mm at night and that the lantern light had a predominant wavelength of 580 nm.

The Impressionist painter Georges Seurat created paintings with an enormous number of dots of pure pigment, each of which was approximately 2.00 mm in diameter. The idea was to have colors such as red and green next to each other to form a scintillating canvas (Fig. P38.17) outside what distance would one be unable to discern individual dots on the canvas? (Assume that A = 500 nm and that the pupil diameter is 4.00 mm.)

A binary star system in the constellation Orion has an angular interstellar separation of 1.00 x 10-5 rad. If = 500 nm, what is the smallest diameter the telescope can have to just resolve the two stars?

A spy satellite can consist essentially of a large-diameter concave mirror forming an image on a digital-camera detector and sending the picture to a ground receiver by radio waves. In effect, it is an astronomical telescope in orbit, looking down instead of up. Can a spy satellite read a license plate? Can it read the date on a dime? Argue for your answers by making an order-of-magnitude calculation, specifying the data you estimate.

A circular radar antenna on a Coast Guard ship has a diameter of 2.10m and radiates at a frequency of 15.0 GHz. Two small boats are located 9.00 km away from the ship. How close together could the boats be and still be detected as two objects?

Grote Reber was a pioneer in radio astronomy. He constructed a radio telescope with a 10.0-m-diameter receiving dish. What was the telescope’s angular resolution for 2.00-m radio waves?

When Mars is nearest the Earth, the distance separating the two planets is 88.6 x 106 km. Mars is viewed through a telescope whose mirror has a diameter of 30.0 cm.

(a) If the wavelength of the light is 590 nm, what is the angular resolution of the telescope?

(b) What is the smallest distance that can be resolved between two points on Mars?

(a) If the wavelength of the light is 590 nm, what is the angular resolution of the telescope?

(b) What is the smallest distance that can be resolved between two points on Mars?

White light is spread out into its spectral components by a diffraction grating. If the grating has 2 000 grooves per centimeter, at what angle does red light of wavelength 640 nm appear in first order?

Light from an argon laser strikes a diffraction grating that has 5 310 grooves per centimeter. The central and first order principal maxima are separated by 0.488 m on a wall 1.72 m from the grating. Determine the wavelength of the laser light.

The hydrogen spectrum has a red line at 656 nm and a blue line at 434 nm. What are the angular separations between these two spectral lines obtained with a diffraction grating that has 4 500 grooves/cm?

A helium–neon laser (A = 632.8 nm) is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5°, what is the spacing between adjacent grooves in the grating?

Three discrete spectral lines occur at angles of 10.09°, 13.71°, and 14.77° in the first-order spectrum of a grating spectrometer.

(a) If the grating has 3 660 slits/cm, what are the wavelengths of the light?

(b) At what angles are these lines found in the second-order spectrum?

(a) If the grating has 3 660 slits/cm, what are the wavelengths of the light?

(b) At what angles are these lines found in the second-order spectrum?

Show that, whenever white light is passed through a diffraction grating of any spacing size, the violet end of the continuous visible spectrum in third order always overlaps with red light at the other end of the second-order spectrum.

A diffraction grating of width 4.00 cm has been ruled with 3 000 grooves/cm.

(a) What is the resolving power of this grating in the first three orders?

(b) If two monochromatic waves incident on this grating have a mean wavelength of 400 nm, what is their wavelength separation if they are just resolved in the third order?

(a) What is the resolving power of this grating in the first three orders?

(b) If two monochromatic waves incident on this grating have a mean wavelength of 400 nm, what is their wavelength separation if they are just resolved in the third order?

The laser in a CD player must precisely follow the spiral track, along which the distance between one loop of the spiral and the next is only about 1.25 /m. A feedback mechanism lets the player know if the laser drifts off the track, so that the player can steer it back again. Figure P38.30 shows how a diffraction grating is used to provide information to keep the beam on track. The laser light passes through a diffraction grating just before it reaches the disk. The strong central maximum of the diffraction pattern is used to read the information in the track of pits. The two first-order side maxima are used for steering. The grating is designed so that the first-order maxima fall on the flat surfaces on both sides of the information track. Both side beams are reflected into their own detectors. As long as both beams are reflecting from smooth non-pitted surfaces, they are detected with constant high intensity. If the main beam wanders off the track, however, one of the side beams will begin to strike pits on the information track and the reflected light will diminish. This change is used with an electronic circuit to guide the beam back to the desired location. Assume that the laser light has a wavelength of 780 nm and that the diffraction grating is positioned 6.90 /m from the disk. Assume that the first-order beams are to fall on the disk 0.400 /m on either side of the information track. What should be the number of grooves per millimeter in the grating?

A source emits 531.62-nm and 531.81-nm light.

(a) What minimum number of grooves is required for a grating that resolves the two wavelengths in the first-order spectrum?

(b) Determine the slit spacing for a grating 1.32 cm wide that has the required minimum number of grooves.

(a) What minimum number of grooves is required for a grating that resolves the two wavelengths in the first-order spectrum?

(b) Determine the slit spacing for a grating 1.32 cm wide that has the required minimum number of grooves.

A diffraction grating has 4 200 rulings/cm. On a screen 2.00 m from the grating, it is found that for a particular order m, the maxima corresponding to two closely spaced wavelengths of sodium (589.0 nm and 589.6 nm) are separated by 1.59 mm. Determine the value of m.

A grating with 250 grooves/mm is used with an incandescent light source. Assume the visible spectrum to range in wavelength from 400 to 700 nm. In how many orders can one see?

(a) The entire visible spectrum and

(b) The short wavelength region?

(a) The entire visible spectrum and

(b) The short wavelength region?

A wide beam of laser light with a wavelength of 632.8 nm is directed through several narrow parallel slits, separated by 1.20 mm, and falls on a sheet of photographic film 1.40 m away. The exposure time is chosen so that the film stays unexposed everywhere except at the central region of each bright fringe.

(a) Find the distance between these interference maxima. The film is printed as a transparency—it is opaque everywhere except at the exposed lines. Next, the same beam of laser light is directed through the transparency and allowed to fall on a screen 1.40m beyond. (b) Argue that several narrow parallel bright regions, separated by 1.20 mm, will appear on the screen, as real images of the original slits. If at last the screen is removed, light will diverge from the images of the original slits with the same reconstructed wave fronts as the original slits produced. (Suggestion: You may find it useful to draw diagrams similar to Figure 38.16. A train of thought like this, at a soccer game, led Dennis Gabor to the invention of holography.)

(a) Find the distance between these interference maxima. The film is printed as a transparency—it is opaque everywhere except at the exposed lines. Next, the same beam of laser light is directed through the transparency and allowed to fall on a screen 1.40m beyond. (b) Argue that several narrow parallel bright regions, separated by 1.20 mm, will appear on the screen, as real images of the original slits. If at last the screen is removed, light will diverge from the images of the original slits with the same reconstructed wave fronts as the original slits produced. (Suggestion: You may find it useful to draw diagrams similar to Figure 38.16. A train of thought like this, at a soccer game, led Dennis Gabor to the invention of holography.)

Potassium iodide (KI) has the same crystalline structure as NaCl, with atomic planes separated by 0.353 nm. A monochromatic x-ray beam shows first-order diffraction maximum when the grazing angle is 7.60°. Calculate the x-ray wavelength.

A wavelength of 0.129 nm characterizes K2 x-rays from zinc. When a beam of these x-rays is incident on the surface of a crystal whose structure is similar to that of NaCl, a first-order maximum is observed at 8.15°. Calculate the interplanar spacing based on this information. If the interplanar spacing of NaCl is 0.281 nm, what is the predicted angle at which 0.140-nm x-rays are diffracted in a first-order maximum?

The first-order diffraction maximum is observed at 12.6° for a crystal in which the interplanar spacing is 0.240 nm. How many other orders can be observed?

In water of uniform depth, a wide pier is supported on pilings in several parallel rows 2.80 m apart. Ocean waves of uniform wavelength roll in, moving in a direction that makes an angle of 80.0° with the rows of posts. Find the three longest wavelengths of waves that will be strongly reflected by the pilings.

Does your bathroom mirror show you older or younger than you actually are? Compute an order-of-magnitude estimate for the age difference, based on data that you specify.

In a church choir loft, two parallel walls are 5.30 m apart. The singers stand against the north wall. The organist faces the south wall, sitting 0.800 m away from it. To enable her to see the choir, a flat mirror 0.600 m wide is mounted on the south wall, straight in front of her. What width of the north wall can she see? Suggestion: Draw a top view diagram to justify your answer.

Determine the minimum height of a vertical flat mirror in which a person 5`10”. In height can see his or her full image. (A ray diagram would be helpful.)

Two flat mirrors have their reflecting surfaces facing each other, with the edge of one mirror in contact with an edge of the other, so that the angle between the mirrors is a. When an object is placed between the mirrors, a number of images are formed. In general, if the angle % is such that na = 360°, where n is an integer, the number of images formed is n - 1. Graphically, find all the image positions for the case n = 6 when a point object is between the mirrors (but not on the angle bisector).

A person walks into a room with two flat mirrors on opposite walls, which produce multiple images. When the person is located 5.00 ft from the mirror on the left wall and 10.0 ft from the mirror on the right wall, find the distance from the person to the first three images seen in the mirror on the left.

A periscope (Figure P36.6) is useful for viewing objects that cannot be seen directly. It finds use in submarines and in watching golf matches or parades from behind a crowd of people. Suppose that the object is a distance p1 from the upper mirror and that the two flat mirrors are separated by a distance h.

(a) What is the distance of the final image from the lower mirror?

(b) Is the final image real or virtual?

(c) Is it upright or inverted?

(d) What is its magnification?

(e) Does it appear to be left–right reversed?

(a) What is the distance of the final image from the lower mirror?

(b) Is the final image real or virtual?

(c) Is it upright or inverted?

(d) What is its magnification?

(e) Does it appear to be left–right reversed?

A concave spherical mirror has a radius of curvature of 20.0 cm. Find the location of the image for object distances of

(a) 40.0 cm,

(b) 20.0 cm, and

(c) 10.0 cm. For each case, state whether the image is real or virtual and upright or inverted. Find the magnification in each case.

(a) 40.0 cm,

(b) 20.0 cm, and

(c) 10.0 cm. For each case, state whether the image is real or virtual and upright or inverted. Find the magnification in each case.

At an intersection of hospital hallways, a convex mirror is mounted high on a wall to help people avoid collisions. The mirror has a radius of curvature of 0.550 m. Locate and describes the image of a patient 10.0 m from the mirror. Determine the magnification.

A spherical convex mirror has a radius of curvature with a magnitude of 40.0 cm. Determine the position of the virtual image and the magnification for object distances of (a) 30.0 cm and

(b) 60.0 cm.

(c) Are the images upright or inverted?

(b) 60.0 cm.

(c) Are the images upright or inverted?

A large church has a niche in one wall. On the floor plan it appears as a semicircular indentation of radius 2.50 m. A worshiper stands on the center line of the niche, 2.00 m out from its deepest point, and whispers a prayer. Where is the sound concentrated after reflection from the back wall of the niche?

A concave mirror has a radius of curvature of 60.0 cm. Calculate the image position and magnification of an object placed in front of the mirror at distances of

(a) 90.0 cm and

(b) 20.0 cm.

(c) Draw ray diagrams to obtain the image characteristics in each case.

(a) 90.0 cm and

(b) 20.0 cm.

(c) Draw ray diagrams to obtain the image characteristics in each case.

A concave mirror has a focal length of 40.0 cm. Determine the object position for which the resulting image is upright and four times the size of the object.

A certain Christmas tree ornament is a silver sphere having a diameter of 8.50 cm. Determine an object location for which the size of the reflected image is three-fourths the size of the object. Use a principal-ray diagram to arrive at a description of the image.

(a) A concave mirror forms an inverted image four times larger than the object. Find the focal length of the mirror, assuming the distance between object and image is 0.600 m.

(b) A convex mirror forms a virtual image half the size of the object. Assuming the distance between image and object is 20.0 cm determine the radius of curvature of the mirror.

(b) A convex mirror forms a virtual image half the size of the object. Assuming the distance between image and object is 20.0 cm determine the radius of curvature of the mirror.

To fit a contact lens to a patient’s eye, a keratometer can be used to measure the curvature of the front surface of the eye, the cornea. This instrument places an illuminated object of known size at a known distance p from the cornea. The cornea reflects some light from the object, forming an image of the object. The magnification M of the image is measured by using a small viewing telescope that allows comparison of the image formed by the cornea with a second calibrated image projected into the field of view by a prism arrangement. Determine the radius of curvature of the cornea for the case p = 30.0 cm and M = 0.013 0.

An object 10.0 cm tall is placed at the zero mark of a meter stick. A spherical mirror located at some point on the meter stick creates an image of the object that is upright, 4.00 cm tall, and located at the 42.0-cm mark of the meter stick.

(a) Is the mirror convex or concave?

(b) Where is the mirror?

(c) What is the mirror’s focal length?

(a) Is the mirror convex or concave?

(b) Where is the mirror?

(c) What is the mirror’s focal length?

A spherical mirror is to be used to form, on a screen located 5.00m from the object, an image five times the size of the object.

(a) Describe the type of mirror required.

(b) Where should the mirror be positioned relative to the object?

(a) Describe the type of mirror required.

(b) Where should the mirror be positioned relative to the object?

A dedicated sports car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When she looks into one side of the hubcap, she sees an image of her face 30.0 cm in back of the hubcap. She then flips the hubcap over and sees another image of her face 10.0 cm in back of the hubcap.

(a) How far is her face from the hubcap?

(b) What is the radius of curvature of the hubcap?

(a) How far is her face from the hubcap?

(b) What is the radius of curvature of the hubcap?

You unconsciously estimate the distance to an object from the angle it subtends in your field of view. This angle θ in radians is related to the linear height of the object h and to the distance d by θ = h/d. Assume that you are driving a car and another car, 1.50 m high, is 24.0 m behind you.

(a) Suppose your car has a flat passenger-side rearview mirror, 1.55 m from your eyes.

How far from your eyes is the image of the car following you?

(b) What angle does the image subtend in your field of view?

(c) What If? Suppose instead that your car has a convex rearview mirror with a radius of curvature of magnitude 2.00 m (Fig. P36.19). How far from your eyes is the image of the car behind you?

(d) What angle does the image subtend at your eyes?

(e) Based on its angular size, how far away does the following car appear to be?

(a) Suppose your car has a flat passenger-side rearview mirror, 1.55 m from your eyes.

How far from your eyes is the image of the car following you?

(b) What angle does the image subtend in your field of view?

(c) What If? Suppose instead that your car has a convex rearview mirror with a radius of curvature of magnitude 2.00 m (Fig. P36.19). How far from your eyes is the image of the car behind you?

(d) What angle does the image subtend at your eyes?

(e) Based on its angular size, how far away does the following car appear to be?

A ball is dropped at t = 0 from rest 3.00 m directly above the vertex of a concave mirror that has a radius of curvature of 1.00m and lies in a horizontal plane.

(a) Describe the motion of the ball’s image in the mirror.

(b) At what time do the ball and its image coincide?

(a) Describe the motion of the ball’s image in the mirror.

(b) At what time do the ball and its image coincide?

A cubical block of ice 50.0 cm on a side is placed on a level floor over a speck of dust. Find the location of the image of the speck as viewed from above. The index of refraction of ice is 1.309.

A flint glass plate (n = 1.66) rests on the bottom of an aquarium tank. The plate is 8.00 cm thick (vertical dimension) and is covered with a layer of water (n = 1.33) 12.0 cm deep. Calculate the apparent thickness of the plate as viewed from straight above the water.

A glass sphere (n = 1.50) with a radius of 15.0 cm has a tiny air bubble 5.00 cm above its center. The sphere is viewed looking down along the extended radius containing the bubble. What is the apparent depth of the bubble below the surface of the sphere?

A simple model of the human eye ignores its lens entirely. Most of what the eye does to light happens at the outer surface of the transparent cornea. Assume that this surface has a radius of curvature of 6.00 mm, and assume that the eyeball contains just one fluid with a refractive index of 1.40. Prove that a very distant object will be imaged on the retina, 21.0 mm behind the cornea. Describe the image.

One end of a long glass rod (n = 1.50) is formed into a convex surface with a radius of curvature of 6.00 cm. An object is located in air along the axis of the rod. Find the image positions corresponding to object distances of

(a) 20.0 cm,

(b) 10.0 cm, and

(c) 3.00 cm from the end of the rod

(a) 20.0 cm,

(b) 10.0 cm, and

(c) 3.00 cm from the end of the rod

A transparent sphere of unknown composition is observed to form an image of the Sun on the surface of the sphere opposite the Sun. What is the refractive index of the sphere material?

A goldfish is swimming at 2.00 cm/s toward the front wall of a rectangular aquarium. What is the apparent speed of the fish measured by an observer looking in from outside the front wall of the tank? The index of refraction of water is 1.33.

A contact lens is made of plastic with an index of refraction of 1.50. The lens has an outer radius of curvature of +2.00 cm and an inner radius of curvature of +2.50 cm. What is the focal length of the lens?

The left face of a biconvex lens has a radius of curvature of magnitude 12.0 cm, and the right face has a radius of curvature of magnitude 18.0 cm. The index of refraction of the glass is 1.44.

(a) Calculate the focal length of the lens.

(b) What If? Calculate the focal length the lens has after is turned around to interchange the radii of curvature of the two faces.

(a) Calculate the focal length of the lens.

(b) What If? Calculate the focal length the lens has after is turned around to interchange the radii of curvature of the two faces.

A converging lens has a focal length of 20.0 cm. Locate the image for object distances of (a) 40.0 cm,

(b) 20.0 cm, and

(c) 10.0 cm. For each case, state whether the image is real or virtual and upright or inverted. Find the magnification in each case.

(b) 20.0 cm, and

(c) 10.0 cm. For each case, state whether the image is real or virtual and upright or inverted. Find the magnification in each case.

A thin lens has a focal length of 25.0 cm. Locate and describes the image when the object is placed

(a) 26.0 cm and

(b) 24.0 cm in front of the lens

(a) 26.0 cm and

(b) 24.0 cm in front of the lens

An object located 32.0 cm in front of a lens forms an image on a screen 8.00 cm behind the lens.

(a) Find the focal length of the lens.

(b) Determine the magnification.

(c) Is the lens converging or diverging?

(a) Find the focal length of the lens.

(b) Determine the magnification.

(c) Is the lens converging or diverging?

The nickel’s image in Figure P36.33 has twice the diameter of the nickel and is 2.84 cm from the lens. Determine the focal length of the lens.

A person looks at a gem with a jeweler’s loupe—a converging lens that has a focal length of 12.5 cm. The loupe forms a virtual image 30.0 cm from the lens.

(a) Determine the magnification. Is the image upright or inverted?

(b) Construct a ray diagram for this arrangement.

(a) Determine the magnification. Is the image upright or inverted?

(b) Construct a ray diagram for this arrangement.

Suppose an object has thickness dp so that it extends from object distance p to p + dp. Prove that the thickness dq of its image is given by (-q2/p2)dp, so that the longitudinal magnification dq/dp = -M2, where M is the lateral magnification.

The projection lens in a certain slide projector is a single thin lens. A slide 24.0 mm high is to be projected so that its image fills a screen 1.80 m high. The slide-to-screen distance is 3.00 m.

(a) Determine the focal length of the projection lens.

(b) How far from the slide should the lens of the projector be placed in order to form the image on the screen?

(a) Determine the focal length of the projection lens.

(b) How far from the slide should the lens of the projector be placed in order to form the image on the screen?

An object is located 20.0 cm to the left of a diverging lens having a focal length f = -32.0 cm. Determine

(a) The location and

(b) The magnification of the image.

(c) Construct a ray diagram for this arrangement.

(a) The location and

(b) The magnification of the image.

(c) Construct a ray diagram for this arrangement.

An antelope is at a distance of 20.0 m from a converging lens of focal length 30.0 cm. The lens forms an image of the animal. If the antelope runs away from the lens at a speed of 5.00 m/s, how fast does the image move? Does the image move toward or away from the lens?

In some types of optical spectroscopy, such as photoluminescence and Raman spectroscopy, a laser beam exits from a pupil and is focused on a sample to stimulate electromagnetic radiation from the sample. The focusing lens usually has an antireflective coating preventing any light loss. Assume a 100-mW laser is located 4.80 m from the lens, which has a focal length of 7.00 cm.

(a) How far from the lens should the sample be located so that an image of the laser exit pupil is formed on the surface of the sample?

(b) If the diameter of the laser exit pupil is 5.00 mm, what is the diameter of the light spot on the sample?

(c) What is the light intensity at the spot?

(a) How far from the lens should the sample be located so that an image of the laser exit pupil is formed on the surface of the sample?

(b) If the diameter of the laser exit pupil is 5.00 mm, what is the diameter of the light spot on the sample?

(c) What is the light intensity at the spot?

Figure P36.40 shows a thin glass (n = 1.50) converging lens for which the radii of curvature are R1 = 15.0 cm and R2 = -12.0 cm. To the left of the lens is a cube having a face area of 100 cm2. The base of the cube is on the axis of the lens, and the right face is 20.0 cm to the left of the lens.

(a) Determine the focal length of the lens.

(b) Draw the image of the square face formed by the lens. What type of geometric figure is this?

(c) Determine the area of the image.

(a) Determine the focal length of the lens.

(b) Draw the image of the square face formed by the lens. What type of geometric figure is this?

(c) Determine the area of the image.

An object is at a distance d to the left of a flat screen. A converging lens with focal length f < d/4 is placed between object and screen.

(a) Show that two lens positions exist that form an image on the screen, and determine how far these positions are from the object.

(b) How do the two images differ from each other?

(a) Show that two lens positions exist that form an image on the screen, and determine how far these positions are from the object.

(b) How do the two images differ from each other?

Figure 36.36 diagrams a cross section of a camera. It has a single lens of focal length 65.0 mm, which is to form an image on the film at the back of the camera. Suppose the position of the lens has been adjusted to focus the image of a distant object. How far and in what direction must the lens be moved to form a sharp image of an object that is 2.00 m away?

The South American capybara is the largest rodent on Earth; its body can be 1.20 m long. The smallest rodent is the pygmy mouse found in Texas, with an average body length of 3.60 cm. Assume that a pygmy mouse is observed by looking through a lens placed 20.0 cm from the mouse. The whole image of the mouse is the size of a capybara. Then the lens is moved a certain distance along its axis, and the image of the mouse is the same size as before! How far was the lens moved?

The magnitudes of the radii of curvature are 32.5 cm and 42.5 cm for the two faces of a biconcave lens. The glass has index of refraction 1.53 for violet light and 1.51 for red light. For a very distant object, locate and describe

(a) The image formed by violet light, and

(b) The image formed by red light.

(a) The image formed by violet light, and

(b) The image formed by red light.

Two rays traveling parallel to the principal axis strike a large plano-convex lens having a refractive index of 1.60 (Fig. P36.45). If the convex face is spherical, a ray near the edge does not pass through the focal point (spherical aberration occurs). Assume this face has a radius of curvature of 20.0 cm and the two rays are at distances h1 = 0.500 cm and h2 = 12.0 cm from the principal axis. Find the difference -x in the positions where each crosses the principal axis.

A camera is being used with a correct exposure at f/4 and a shutter speed of (1/16) s. In order to photograph a rapidly moving subject, the shutter speed is changed to (1/128) s. Find the new f -number setting needed to maintain satisfactory exposure.

A nearsighted person cannot see objects clearly beyond 25.0 cm (her far point). If she has no astigmatism and contact lenses are prescribed for her, what power and type of lens are required to correct her vision?

The accommodation limits for Nearsighted Nick’s eyes are 18.0 cm and 80.0 cm. When he wears his glasses, he can see faraway objects clearly. At what minimum distance is he able to see objects clearly?

A person sees clearly when he wears eyeglasses that have a power of -4.00 diopters and sit 2.00 cm in front of his eyes. If the person wants to switch to contact lenses, which are placed directly on the eyes, what lens power should be prescribed?

A lens that has a focal length of 5.00 cm is used as a magnifying glass.

(a) To obtain maximum magnification, where should the object be placed?

(b) What is the magnification?

(a) To obtain maximum magnification, where should the object be placed?

(b) What is the magnification?

The distance between eyepiece and objective lens in a certain compound microscope is 23.0 cm. The focal length of the eyepiece is 2.50 cm, and that of the objective is 0.400 cm. What is the overall magnification of the microscope?

The desired overall magnification of a compound microscope is 140/. The objective alone produces a lateral magnification of 12.0X. Determine the required focal length of the eyepiece.

The Yerkes refracting telescope has a 1.00-m diameter objective lens of focal length 20.0 m. Assume it is used with an eyepiece of focal length 2.50 cm.

(a) Determine the magnification of the planet Mars as seen through this telescope.

(b) Are the Martian polar caps right side up or upside down?

(a) Determine the magnification of the planet Mars as seen through this telescope.

(b) Are the Martian polar caps right side up or upside down?

Astronomers often take photographs with the objective lens or mirror of a telescope alone, without an eyepiece.

(a) Show that the image size h` for this telescope is given by h` = f h/ (f - p) where h is the object size, f is the objective focal length, and p is the object distance.

(b) What If? Simplify the expression in part (a) for the case in which the object distance is much greater than objective focal length.

(c) The “wingspan” of the International Space Station is 108.6 m, the overall width of its solar panel configuration. Find the width of the image formed by a telescope objective of focal length 4.00 m when the station is orbiting at an altitude of 407 km.

(a) Show that the image size h` for this telescope is given by h` = f h/ (f - p) where h is the object size, f is the objective focal length, and p is the object distance.

(b) What If? Simplify the expression in part (a) for the case in which the object distance is much greater than objective focal length.

(c) The “wingspan” of the International Space Station is 108.6 m, the overall width of its solar panel configuration. Find the width of the image formed by a telescope objective of focal length 4.00 m when the station is orbiting at an altitude of 407 km.

Galileo devised a simple terrestrial telescope that produces an upright image. It consists of a converging objective lens and a diverging eyepiece at opposite ends of the telescope tube. For distant objects, the tube length is equal to the objective focal length minus the absolute value of the eyepiece focal length.

(a) Does the user of the telescope see a real or virtual image?

(b) Where is the final image?

(c) If a telescope is to be constructed with a tube of length 10.0 cm and a magnification of 3.00, what are the focal lengths of the objective and eyepiece?

(a) Does the user of the telescope see a real or virtual image?

(b) Where is the final image?

(c) If a telescope is to be constructed with a tube of length 10.0 cm and a magnification of 3.00, what are the focal lengths of the objective and eyepiece?

A certain telescope has an objective mirror with an aperture diameter of 200 mm and a focal length of 2 000 mm. It captures the image of a nebula on photographic film at its prime focus with an exposure time of 1.50 min. To produce the same light energy per unit area on the film, what is the required exposure time to photograph the same nebula with a smaller telescope, which has an objective with a diameter of 60.0 mm and a focal length of 900 mm?

The distance between an object and its upright image is 20.0 cm. If the magnification is 0.500, what is the focal length of the lens that is being used to form the image?

The distance between an object and its upright image is d. If the magnification is M, what is the focal length of the lens that is being used to form the image?

Your friend needs glasses with diverging lenses of focal length - 65.0 cm for both eyes. You tell him he looks good when he doesn’t squint, but he is worried about how thick the lenses will be. Assuming the radius of curvature of the first surface is R1 = 50.0 cm and the high-index plastic has a refractive index of 1.66,

(a) Find the required radius of curvature of the second surface.

(b) Assume the lens is ground from a disk 4.00 cm in diameter and 0.100 cm thick at the center. Find the thickness of the plastic at the edge of the lens, measured parallel to the axis. Suggestion: Draw a large cross-sectional diagram.

(a) Find the required radius of curvature of the second surface.

(b) Assume the lens is ground from a disk 4.00 cm in diameter and 0.100 cm thick at the center. Find the thickness of the plastic at the edge of the lens, measured parallel to the axis. Suggestion: Draw a large cross-sectional diagram.

A cylindrical rod of glass with index of refraction 1.50 is immersed in water with index 1.33. The diameter of the rod is 9.00 cm. The outer part of each end of the rod has been ground away to form each end into a hemisphere of radius 4.50 cm. The central portion of the rod with straight sides is 75.0 cm long. An object is situated in the water, on the axis of the rod, at a distance of 100 cm from the vertex of the nearer hemisphere.

(a) Find the location of the final image formed by refraction at both surfaces.

(b) Is the final image real or virtual? Upright or inverted? Enlarged or diminished?

(a) Find the location of the final image formed by refraction at both surfaces.

(b) Is the final image real or virtual? Upright or inverted? Enlarged or diminished?

A zoom lens system is a combination of lenses that produces a variable magnification while maintaining fixed object and image positions. The magnification is varied by moving one or more lenses along the axis. While multiple lenses are used in practice to obtain high-quality images, the effect of zooming in on an object can be demonstrated with a simple two-lens system. An object, two converging lenses, and a screen are mounted on an optical bench. The first lens, which is to the right of the object, has a focal length of 5.00 cm, and the second lens, which is to the right of the first lens, has a focal length of 10.0 cm. The screen is to the right of the second lens. Initially, an object is situated at a distance of 7.50 cm to the left of the first lens, and the image formed on the screen has a magnification of +1.00.

(a) Find the distance between the object and the screen.

(b) Both lenses are now moved along their common axis, while the object and the screen maintain fixed positions, until the image formed on the screen has a magnification of +3.00. Find the displacement of each lens from its initial position in (a). Can the lenses be displaced in more than one way?

(a) Find the distance between the object and the screen.

(b) Both lenses are now moved along their common axis, while the object and the screen maintain fixed positions, until the image formed on the screen has a magnification of +3.00. Find the displacement of each lens from its initial position in (a). Can the lenses be displaced in more than one way?

The object in Figure P36.62 is midway between the lens and the mirror. The mirror’s radius of curvature is 20.0 cm, and the lens has a focal length of -16.7 cm.

Considering only the light that leaves the object and travels first toward the mirror, locate the final image formed by this system. Is this image real or virtual? Is it upright or inverted? What is the overall magnification?

Considering only the light that leaves the object and travels first toward the mirror, locate the final image formed by this system. Is this image real or virtual? Is it upright or inverted? What is the overall magnification?

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