Energy on the Move Unit Notes Chapter 10: Waves
I. The Nature of Waves
a. What’s in a wave?—a wave is a repeating disturbance or movement that transfers energy through matter or space.
b. Waves and Energy—a pebble falling into water transfers some of its energy to the particles of water, the particles of water transfer their energy to nearby particles of water causing them to move, too.
i. Waves and matter—all waves have the property of carrying energy without transporting matter…boat and buoys just bob…they don’t actually move anywhere.
ii. Making waves—waves do not travel when they no longer have energy to carry. If you make a wave in a rope by moving your hand up and down, the rope will carry the energy of the wave. If you stop moving your hand up and down, the wave will stop. The vibration provides the energy necessary to start the wave. c. Mechanical Waves—waves that travel only through matter. Ocean waves have water as
their medium—the matter that waves travel through. Some waves, like light and radio waves, can travel through space.
i. Transverse waves—matter in the medium moves back and forth at right angles to the direction the wave travels (a wave in water does this)
ii. Compressional waves—the medium moves back and force in the same direction that the wave travels. (a spring toys does this)
iii. Sound waves—are compressional waves that squeeze air molecules closer and further apart.
iv. Sound and Other Materials—this works for wood and water, too…other mediums.
v. Water waves—not purely transverse waves…the compression of water waves also moves the water molecules back and forth a short distance, not as far as air molecule compression. This means that floating objects on a water wave actually move in circles. Wind blowing across the water surface causes waves to form.
also travel across the crust. The seismic waves, like water waves, have compressional character and transverse character.
Self Check p. 295 Answers: 1) possible answers include that transverse waves move a right angles to the direction the waves travel, while compression waves move back and forth in the same direction as the wave travels. Water waves are partly transverse waves. Sound waves are compression waves. 2) A buoy moves up and down when a wave passes. The wave does not move the buoy forward. 3) Pull the ends of the toy apart and anchor them firmly at both ends. Then, squeeze several coils together at one end and release them. 4) Mechanical waves are either transverse or compressional, but always require a medium to travel through. 5) The tide and its related current will move unanchored boats. 6) 6 seconds.
Good websites to learn from:
http://en.wikipedia.org/wiki/Wave (way technical)
http://www.itsscience.com/waves/index.htm (a physical science teacher’s page)
http://www.onr.navy.mil/Focus/ocean/motion/waves1.htm (oceanography)
II. Wave Properties
a. The Parts of a Wave—waves have different characteristics. We have specialized words to describe wave characteristics to tell waves apart.
Crests—high points in transverse waves. Troughs—low points in transverse waves.
Compressions—dense points in compressional waves. Rarefactions—spread-out points in a compressional wave.
b. Wavelength—the distance between one point on a wave and the nearest point just like it. In transverse waves the wavelength is the distance between two crests or the distance between troughs. In a compressional wave, the wavelength is the measure from the start of a compression to the start of the next compression (or from the start of a rarefraction to the start of the next rarefraction).
c. Frequency and Period—when you tune a radio you are choosing which waves to receive. Specifically, you are choosing the frequency of the waves. The frequency describes the number of wavelengths that pass a fixed point each second. (you are counting waves per second). A frequency of 1Hz means that one wavelength passes by you in 1s (this is also known as cycles/sec). The period of a wave is the inverse of the frequency. In other words, the period is the length of time it takes for one wave to pass a point
i. Wavelength is related to frequency—if you make a transverse wave with a rope, you can increase the frequency by moving the rope up and down faster. This also makes the wavelength shorter. This is true for all waves: higher frequency means shorter wavelength. If you move the rope up and down in 1 second…you have vibrated the string at 1 Hz (cycle per second). If you can do it 5 times in one second, you have a 5 Hz wave.
d. Wave Speed—light waves travel much faster than sound waves. Also, waves that travel through matter have different speeds depending on the type of matter and the
conditions of the matter.
i. Calculating wave speed—v = f x λ V = wave speed (velocity)
F = frequency (Hz)
Λ = wavelength (meters…usually)
Practice problems p. 299 Answers: 1) 1,500 m/s 2) 17m 3) 20,000Hz 4) The wavelength in water is 15m, and the wavelength in air is 3.4 m; so the wavelength in water is 4.4 times the wavelength in air.
e. Amplitude and Energy—the amount of energy a wave can carry is related to the amplitude of the wave. The higher the amplitude, the more energy a wave is carrying.
i. Amplitude of Compressional waves—is related to how compressed the compression and how rarefied the rarefaction. The more dense the
compressions, the higher the amplitude. The less dense the rarefaction, the higher the wave amplitude.
ii. Amplitude of Transverse waves—the higher the crest, the higher the amplitude. The lower the trough, the higher the amplitude. The amplitude is measured by the distance from the bottom of the trough to the rest position OR the top of the crest down to the rest postion.
Self Check p. 301 Answers: 1) A compression wave with a large amplitude has particles of medium closer together in compression and farther apart in rarefactions. 2) the wavelength decreases. 3) as the period increases, the frequency decreases 4) the particles in a solid are more closely packed, so that collisions between particles occur more frequently than in a gas, where particles are farther apart. 5)To make the wavelength shorter, increase the frequency of the weave by shaking the end of the rope up and down more rapidly. To increase the amplitude, increase the distance the end of the rope is moved up and down. 6) f = v/λ = (4.0 m/s) / (0.5m) = 8.0 Hz 7) λ = v/f = (300,000,000 m/s) / (100,000,000 Hz) = 3.0 m
a. Reflection—sound echoes—that’s reflection of wave energy. Your image in a mirror— that’s reflection, too. The steps for seeing your image in a mirror: 1) light bounces off of your face 2) then light from your face bounces off the mirror back into your eyes.
i. Echoes—animals use the bouncing of sound waves to learn about their surroundings…bats and dolphins...actually humans do this, too. You just don’t think of it that way (if someone yells, how do you know which way to look0 ii. The Law of Reflection—beam striking a surface is the incident beam. The beam
that is reflected is called the reflected beam. A line drawn perpendicular from the surface is the called the “normal”. The angle of incidence (i) is the measure of the angle between the incident beam and normal. The angle of reflection (r) is the measure of the angle of the reflected beam with normal. The angle of incidence is always equal to the angle of reflection.
b. Refraction—Ever notice what happens when you look through clear water at objects at the surface…or look at objects in a pool from the surface? A wave’s speed depends on the medium…if a wave enters a new medium, the new speed causes a change in the speed of the wave. If the wave is traveling at an angle when it passes from one medium to another, it changes directions…it bends. Refraction is the bending effect caused by the speed change of waves as they pass through different mediums.
Refracting toward normal—a beam passing from a fast medium into a slower medium bends toward normal.
Refracting away from normal—a beam passing from a slow medium into a faster medium bends away from normal.
i. Refraction of Light in Water—light waves reflection from a swimmer’s foot are refracted away from normal and enter your eyes. Your brain assumes that all light waves have traveled in a straight line. The light waves that enter your eyes seem to have come from a foot that was higher in the water.
c. Diffraction—when waves strike an object they can bounce off (be reflected). If the object is transparent, the light waves will be refracted as they pass through (refraction). Waves can bend around an object. Diffraction occurs when an object causes a wave to change direction and bend around it. Refraction—bending caused when waves pass through. Diffraction—bending caused when waves pass around.
ii. Hearing around corners—sounds around corners happens because sound waves bend around the opening…sound waves have a much larger wavelength than light waves. Sound waves diffract around the door and spread out down the hallway. Light waves have a much shorter wavelength…they don’t bend around the door and spread down the hallway.
iii. Diffraction of radio waves—AM radio has much longer wavelengths and FM radio. For this reason, AM radio waves will diffract around objects and FM radio waves will not. AM reception can be much better than FM reception around obstacles and hills.
d. Interference—if two waves meet at the same place and time, they will combine and form a new wave that is different than the others. When two or more waves overlap and combine to form a new wave this is called interference.
i. Constructive interference—amplitude of the new wave is equal to the sum of the amplitudes of the original wave. This is the same for transverse and compressional waves…these types of waves are said to be “in phase”.
ii. Destructive Interference—this happens when the the creast of one transverse wave meets the trough of another transverse wave…these waves are “out of phase”. The resulting wave is the difference between the amplitudes of the overlapping waves. This happens in compressional waves, too. In sound waves, destructive interferences results in a reduction in loudness.
e. Standing Waves—interference of two identical waves makes a vibration where the troughs and crests appear to be not moving. A standing wave—a special type of wave pattern that forms when waves equal in wavelength and amplitude, travel in opposite directions and continually interfere with each other. The places where the two waves completely cancel each other out is called a NODE. The wave vibrates between the nodes.
i. Standing waves and music—standing waves are the reason that we can hear music
f. Resonance—objects (like tuning forks and instruments) have natural frequencies when they vibrate. If you happen to send a strong sound wave that is at the same frequency as the tuning fork, the tuning fork will suddenly vibrate.
make it vibrate—sound energy to mechanical energy 4) Students’ drawings should show objects deeper than they actually are.
Chapter 11: Sound
I. The Nature of Sound
a. What causes sound?—all sound is produced by something that vibrates.
b. Sound Waves—the process of collision and energy transfer creates a compressional wave called a sound wave.
i. Traveling as a wave—compressions and rarefactions move away from the speaker as molecule in the air collide with their neighbor molecules.
c. The speed of Sound—as long as there is matter to travel through, sound can do it. In a vacuum, sound cannot travel.
i. The speed of sound in different materials—the speed of sound depends on the medium that it is traveling through and whether the medium is solid, liquid or gas. At room temp sound travels 347 m/s through air, 1,498 m/s in water, 4,877 m/s through aluminum. Slow in gases, faster in liquids, fastest in solids…in general. The speed depends upon the closeness of particles in the matter.
ii. A model for transmitting sound—passing a bucket analogy with people far apart of closer together. The bucket represents a compression wave. Pictures p. 324.
iii. Temperature and the Speed of Sound—sound travels faster through matter that is hotter…faster moving particles mean collisions are more likely. d. Human Hearing---4 stages of making sense of sound transmissions
1) The ear gathers the compressional waves
2) The compressional waves are amplified (by ear drum and bones)
4) The brain decodes and interprets the impulses.
ii. Gathering sound waves—the outer ear—the outer ear is the visible part of the ear, the ear canal, and eardrum. Sound is captured and directed.
iii. Amplifying sound waves—the middle ear—the tiny bones start to vibrate. These bones have a lever system that multiplies the force and pressure exerted by the wave. (hammer, anvil, and stirrup) The stirrup vibrates the oval window… mysterious.
iv. Converting sound waves—the inner ear—the cochlea receives the stirrup vibrations through the oval window. The cochlea is filled with liquid that vibrates with the sound. Small hairs on the surface of the cochlea covert sound waves to nerve impulses.
Self Check p. 326 Answers: 1) Your vocal cords create compressions and rarefactions in air molecules that travel out in all directions 2) Sound travels faster in liquids than in gas because the molecules in liquid are closer to one another than are the molecules in gas. 3) Increased temperature make molecules within the medium move more feely, which make them collide more frequently with other molecules 4) The outer ear collects sound waves. Bones in the middle ear amplify sound waves and vibrate the oval window. This causes hairs in the cochlea of the middle ear to vibrate. The cochlea sends information about the vibrations as nerve impulses to the brain. 5) Possilbe answers: hair clees vibrate even when no sound is present, damage to nerve cells. 6) 1000m/(331 m/s)= 3.02s 7) 1000m/(343m/s) = 2.92s
II. Properties of Sound
a. Intensity and Loudness—more energy is transferred to the medium when the particle of the medium are forced closer together in the compressions and spread farther apart in the rarefactions.
i. Intensity—a measure of the amount of energy that flow through a certain area in a specific amount of time. Intensity influences how far away a sound can be heard.
ii. Intensity Decreases With Distance—some of the wave’s energy is converted to other forms of energy as a wave travels during the collision of particles.
Analogy: think about how a basketball bounces (bouncy ball)
iv. The Decibel Scale—a measurement scale called decibels (dB), help measure the differences in intensity. Sounds with intensity levels above 120dB may cause pain and permanent hearing loss. dB scale on Fig. 7 p. 329
b. Pitch—related to frequency
i. Frequency and pitch—freq in sound is the number of compressions or the number or rarefactions that pass by each second. Your brain interprets fast vibrations as a sound with a high pitch. Frequency is a numerical measure. Pitch is you brain’s interpretation of frequency. The healthy human ear can hear sounds in the 20Hz to 20,000Hz range. The ear is most sensitive to 440Hz and 7000Hz where we can hear much fainter sounds.
Mr. Schmidt’s Frequency and Volume Results from the Gizmo Frequency, dB
30, -9 60, -13 125, -21 250, -39 500, -63 1000, -68 2000, -70 4000, -67 8000, -65 16000, -22
ii. Ultrasonic and Infrasonic waves—ultrasonic sounds above 20,000 Hz have medical applications and underwater applications. Bats and dogs can hear ultrasonic sounds. Infrasonic (AKA sub-sonic), you may not be able to hear these waves, and you might be able to feel them in your body.
c. The Doppler Effect—a race car passes you or a police car—you experience different pitches as the sound passes by you. The change in pitch (or wave frequency) due to a moving wave source is called the Doppler effect.
ii. A moving observer—similar as above except that the observer is moving and the sound is stationary.
iii. Using the Doppler Effect—Radar guns use the Doppler effect with
electromagnetic radiation to measure the speed of a car. The radar frequency shifts depending on the speed and direction of the moving car. This is also used for weather reporting.
Self Check p. 332 Answers: 1) intensity; amplitude, loudness 2) range of human hearing: 0 dB and above; level damaging to human ears: 120 dB 3) Frequency is a measure of how many wavelengths pass a point each second. Pitch is how high or low a sound seems to be. As frequency increase, pitch gets higher. 4) Sketches should show that the wavelength of compressions decreases as a moving object comes near and increases as the moving object moves away. 5) the race care is moving faster so the Doppler shift is greater. 6) Check students’ table; the higher the frequency the greater the number of wavelengths that pass you in a second.
III. Music (May not be assigned) Self Check p. 337 Answers: 1)
IV. Using Sound (May not be assigned Self Check p. 343 Answers: 1)
Chapter 12: Electromagnetic Waves I. What are electromagnetic waves?
a. Waves in Space—electromagnetic waves are all around you…some passing through you. i. Sound and water waves—need matter to propagate
ii. Electromagnetic waves—do not need matter-they travel through space. Electromagnetic waves are made by vibrating electric charge and can travel through space where matter is not present.
i. Magnetic fields and moving charges—remember, moving charges also create magnetic fields.
ii. Changing Electric and Magnetic Fields—a changing magnetic field creates a changing electric field. For example, in a transformer, changing electric current in the primary coil produces a changing magnetic field. This changing magnetic field then creates a changing electric field in the secondary coil that produces current in the coil.
c. Making Electromagnetic Waves—when an electric charge vibrates, it generates an electromagnetic wave (in the same way that a speaker vibrates to generate a
compressional sound wave). A vibrating charge is surrounded by changing electric field and changing magnetic fields. Electric field in turn generate magnetic fields. They go back and forth generating eachother through space. Transverse waves because the magnetic fields vibrate at right angles to the direction the wave travels. These are 3 dimensional waves.
d. Properties of Electromagnetic Waves—All objects emit electromagnetic waves since all matter is made of vibrating particles. Electromagnetic waves from the Sun cause electrons in your skin to vibrate and gain energy, The energy carried by an
electromagnetic wave is called radiant energy. Radiant energy makes a fire feel warm and enables you to see.
i. Wave speed—all electromagnetic radiation travels at speeds of 300,000 km/s in the vacuum of space. This is usually called the “speed of light” since light is a form of electromagnetic radiation. Electromagnetic waves usually travel more slowly in solids and more quickly in gases (opposite of mechanical waves). ii. Wavelength and frequency—this is the same as in the waves chapter. Waves
here have the same relationship. Calculating wave speed—v = f x λ V = wave speed (velocity)
F = frequency (Hz)
Λ = wavelength (meters…usually) e. Waves and Particles—
ii. Particles as waves—Later, scientists realized that particles, such as electrons, also had wave-like properties (refractions, diffraction, and reflection). This led scientists to realize that all particles, not only electrons, have wave-like properties.
Self Check p. 359 Answers: 1) The vibrating electric and magnetic fields that create electromagnetic waves are perpendicular to the direction the wave travels. A compressional wave causes a disturbance that moves back and forth along the direction the wave travels. 2) They are equal. 3) by causing charge particles within objects to move. 4) An electromagnetic wave is made of vibrating electric and magnetic fields that continually produce each other; matter is not needed for this to occur 5) No, an
electromagnetic wave would not be produced. Both a vibrating electric and magnetic field are needed to produce an electromagnetic wave that travels away from the vibrating charge. 6) 500s = 8.33 min 7) 2.502 x 1010 km
II. The Electromagnetic Spectrum Some awesome websites:
http://imagine.gsfc.nasa.gov/docs/science/know_l1/emspectrum.html (good ideas)
http://en.wikipedia.org/wiki/Electromagnetic_radiation (very technical)
www.bjpinchbeck.com (under the science link, look for physics, these sites are good. I trust BJ Pinchbeck…so far)
a. A Range of Frequencies—there is a very wide range of frequencies of EM waves. b. Radio Waves—radio waves do not create compression and rarefactions. The radio
device ‘transforms’ the EM waves into compressional waves through a speaker. i. Microwaves—radio waves are low frequency EM waves with wavelengths
longer than 1 meter. The portion of the radio waves with wavelengths of about 30cm are called microwaves. From 1cm -20cm microwaves are used for communication—cell phones and satellites. A certain frequency of microwaves can cause water molecules to vibrate billions of times each second…this generates a great deal of thermal energy.
iii. Magnetic Resonance Imaging (MRI)—powerful magnets, a radio wave emitter, and a radio wave detector is used together to painlessly create images of the inside of a patient’s body.
c. Infrared Waves—warmth from a fire is thermal energy transmitted to you by infrared waves---a type of electromagnetic wave with wavelengths between 1 mm and about 750 billionths of a meter. Every object emit infrared waves…hotter objects emit more infrared waves than cooler objects. This is useful…list of uses on p. 362.
d. Visible Light—is the range of electromagnetic waves that you can detect with your eyes. Visible light has wavelengths around 750 billionths of a meter to 400 billionths of a meter. Our eyes detect differences in light wavelength. Short wavelength light looks blue ---long wavelength light looks red.
e. Ultraviolet Waves—400 billionths of a meter to 10 billionths of a meter wavelengths have enough energy to enter your skin and cause damage. UVA (longer wavelength) and UVB (shorter wavelength) are types of ultraviolet radiation that reach the Earth’s surface. These can cause cancer…and are also needed for your skin to produce the vitamin D that you need to survive.
i. Useful UVs—UV can kill bacteria because it can disrupt DNA molecules and proteins, so they can be used to sanitize medical equipment. UV can also make some things fluoresce. This is used to help fight crime…finding fingerprints. ii. The ozone layer—Ozone (O3) is constantly being formed and destroyed by UV
waves high in the atmosphere. This absorbs the bulk of very high energy UV waves that come from the sun. The depletion causes serious problems on our planet.
f. X Rays and Gamma Rays—the shortest wavelengths of EM wave (highest frequency). Xrays have wavelengths between ten billionths of a meter and ten trillionths of a meter. Low doses of Xray can help doctors see your bones…an examine luggage.
Wavelengths smaller than 10 trillionths of a meter are called gamma rays. Gamma rays are produced by atomic nuclear reactions. Xrays and gamma rays can be used to kill cancerous cells.
III. Radio Communication (May not be assigned) Self Check p. 373 Answers: 1)
Chapter 13: Light
I. The Behavior of Light
a. Light and Matter—you can only see an object if it reflect light.
i. Opaque, transparent, and translucent—opaque--absorbs and reflects light—no light passes through it. Translucent—light passes partially through. Transparent —you can see the object clearly…light passes through clearly.
b. Reflection of Light—occurs when light wave strikes an object and bounce off.
i. The law of reflection—the angle that light strikes a surface is the same as the angle at which it is reflected (see other notes)
ii. Regular and diffuse reflection—parallel rays reflected back to your eyes gives you a good image. An uneven surface will reflect light at many different angles causing a diffuse reflection.
iii. Roughness of surfaces—to cause a regular reflection, the roughness of the surface must be less than the wavelengths it reflects.
c. Refraction of Light—this is the bending properties of light that we discussed in the waves chapter.
i. Index of refraction—the amount of bending that takes place depends on the speed of light through the material. ---the index is a property of the material that indicates how much the speed of light in the material is reduced. The larger the index, the more light is slowed (and bent) by the material.
ii. Prisms—white light, such as sunlight, is made up of this whole range of
wavelengths. A triangular prism refracts light twice—when it enters and when it leaves. Longer wavelengths are refracted more than the shorter wavelengths, the light gets separated into all of its component wavelength colors.
iii. Rainbows—rain droplets are refracting light.
Self Check p. 384 Answers: 1) transparent materials (clear glass) transmit all light, opaque materials (a wall) transmit no light, and translucent materials (waxed paper) transmit some light 2) Smooth surfaces reflect parallel rays in one direction; rough surfaces reflect parallel rays in many directions. 3) Mirages are cause by refraction of light through air layers of different densities. On a hot day, air near the ground is warmer and less dense than air above it. This causes a light refraction that gives the appearance of a puddle of wavy water. 4) The different wavelength of light in it are bent different amounts, causing a rainbow effect. 5) The lens is transparent, the fingernail and skin are translucent, the tooth is opaque. 6) 48o 7) 27o
II. Light and Color—
a. Colors-- you see color because light is reflected back to your eyes has not been
absorbed by the object that you are seeing. Black objects absorb almost all of the colors present in visible light.
i. Colored filters—filters transmit one or more colors of light but absorb all others. The color of the filter is the color transmitted.
ii. Looking through colored filters—(see pictures on page 390) b. Seeing Color—
i. Light and the Eye—light is focused on the retina in your eye. Two types of cells on the retina absorb light. The cells absorb light energy and convert it to the brain. Cones help you see color mostly in the daytime.
ii. Cones and rods—three different cones…red respond to red and yellow; green cones respond to yellow and green; blue cones respond to blue and violet. A second type of cell called a rod is sensitive to dim light and helps with night vision.
iii. Interpreting color—
iv. Color blindness—if one of your sets of cones did not function properly, you would not be able to distinguish between certain colors. 8% of men and 0.5% of women have this condition called color-blindness.
c. Mixing Colors—a pigment is a colored material that is used to change the color of other substances. The color of a pigment results from the different wavelengths of light that the pigment reflects.
ii. Paint pigments—mixing paint pigments is different than mixing different colors of light.
iii. Mixing pigments—three primary pigments are magenta (bluish red), cyan (greenish blue), and yellow. The three primary pigments product black instead of white because they absorb all colors.
Self Check p. 389 Answers: 1) red is reflected and all others are absorbed 2) primary colors of light are red, green, and blue. Primary colors of pigment are magenta, cyan, and yellow 3) not all of their cone cells function properly (their cone cells function differently). 4) The fence reflects all colors of visible light. Since all the cones in your eyes are stimulated, you see white. 5) It will appear black
III. Producing Light (May be assigned) Self Check p. 399 Answers: 1)
IV. Using Light (May not be assigned) Self Check p. 404 Answers: 1)
Chapter 14: Mirrors and Lenses I. Mirrors
a. How do you use light to see?—When no light reflects from an object to your eye, your eyes cannot see anything.
i. Light rays—light sources send out waves in all directions. Your brain interprets light waves as if they travel in a single direction.
b. Seeing Reflections with Plane Mirrors—a flat smooth mirror called a plane is the one you use most of the time.
i. Reflection form plane mirrors—if you were 1 m from the mirror, your image would appear to be 1 m behind the mirror, or 2 m from you. In fact, your image is what someone standing 2 m from your would see.
off the of the mirror come from a point behind the mirror. Because the image appears to be behind the mirror---even though there is nothing behind the mirror, this is called a virtual image.
c. Concave Mirrors—mirror curved inward
i. Features of concave mirrors—the optical axis is an imaginary straight line drawn perpendicular to the surface of the mirror at its center. Every light ray traveling parallel to the optical axis is reflected back to a point on the optical axis called the focal point. Light traveling through the focal point is reflected parallel to the optical axis. The distance from the focal point to the center of the mirror is the focal length.
ii. How a concave Mirror works—the image in the mirror changes depending on the object location relative to the focal point of the mirror. This is complicated and needs a diagram and a careful reading of p. 419.
iii. Real images—a real image is formed when light rays converge to form the image. You could hold a piece of paper at the location of a real image and see the image project on the paper. When an object is farther from a concave mirror than twice the focal length, the image that is formed is real, smaller, and upside down, or inverted.
iv. Creating Light Beams—By placing a light at the focal point, all of the light is reflected in a concentrated beam with nearly parallel rays.
v. Mirrors that magnify—The image formed by a concave mirror changes again when the object is placed between the focal point and the mirror. A virtual image results…it appears behind the mirror and it is larger and upright. d. Convex mirrors—a mirror that curves outward. The reflected rays diverge and never
meet, so the image formed by a convex mirror is a virtual image. The image is upright and smaller than the actual object.
i. Uses of Convex Mirrors—these mirrors have a wide field of view. Convex mirrors can widen the view of traffic that can be seen in a rearview or side-view mirror. However the image created by a convex mirror is smaller than the actual object, so this compromises your sense of distance…”Objects in mirror are closer than they appear”. (Objects In Mirror Appear Farther than they Actually Are)
Self Check p. 422 Answers: 1) Your image moves toward you and becomes larger 2) Sketches should show light rays from a single point on the object diverging after being reflected from the mirror. 3) The object is more than two focal lengths from the mirror, so the image is real, smaller, and inverted 4) The image gets smaller. 5) Yes, the virtual image formed by the convex mirror in Figure 8 has been
photographed. 6) 30o
II. Lenses
a. What is a lens?—a lens is a transparent material with at least one curved surface that causes light rays to bend (refract) as they pass through. They can be convex or concave. b. Convex lenses—thicker in the middle than at the edges. Light waves that travel parallel
to the optical axis are refracted toward the center of the lens. They pass through a single point called the focal point. The focal length depends on the shape of the lens. Light rays traveling along the optical axis are not bent at all. (see images on page 425 to see this complicated information)
i. Forming images with a convex lens--(see images on page 425 to see this complicated information) if the object is more than two focal lengths from the lens, the image is real, reduced, and inverted, and on the opposite side of the lens from the object. As the object moves closer to the lens, the image gets larger. When the object is between 1 and 2 focal lengths, the image is larger and still inverted. When the object is less than one focal length from the lens, the image becomes an enlarged virtual image. The image is virtual because light rays from the object diverge after that pass through the lens. Convex lenses are used as magnifying glasses…the large upright virtual image actually appears behind the object. The object is closer than one focal length.
c. Concave lenses—A concave lens is thinner in the middle and thicker at the edges. Light rays bend outward, away from the optical axis. These never form a real image…there is no focal point. Concave lenses are usually used in combination with other lenses (in telescopes and some types of glasses).
Image summary table on page 427.
i. Focusing on near and far—for an image to be formed on the retina, the focal length of the lens needs to be changed. The lens in your eye is flexible, and muscles flex the lens to change its focal length.
e. Vision problems—
i. Farsightedness—a person who is farsighted can see distant objects clearly, but can’t bring nearby objects into focus. Close-up objects cannot form a sharp image on the retina. The problem can be correct by using a convex lens that bends light rays so they are less spread out before they enter the eye. Farsightedness tends to happen as the lens loses flexibility with age.
ii. Astigmatism—occurs when the surface of the cornea is curved unevenly. Their corneas are more oval than round in shape. This causes blurry images at a distance. Corrective lenses also have an uneven curvature, canceling out the effect of an uneven cornea.
iii. Nearsightedness—a person can see object clearly at a close distance. They have trouble focusing on objects at a far distance. To correct the problem,
nearsighted people can wear concave lenses that cause the waves of light to diverge before the light enters the eye…this allows the image to focus closer to the retina.
Self Check p. 431 Answers: 1) the focal length increases as the sides of the lens become less curved 2) The image less than one focal length is enlarged, upright, and virtual. The image more than two focal lengths from the lens is reduced, inverted and real 3) The image formed by a concave lens is always reduced, upright, and virtual 4) As the eye focuses on a nearby object, the lens in the eye becomes more curved, and its focal length decreases. 5) Light rays from the light source will be refracted by the lens so they travel parallel to the optical axis. A beam of light will be formed. 6) A real, inverted, enlarge image is formed if the object is between one and two focal lengths from the lens. So the maximum distance from the lens would be two focal lengths or 30 cm.
