Transcript light
4/22 do now – on a new sheet • A car travels 80. meters due north in 15 seconds. Then the car turns around and travels 40. meters due south in 5.0 seconds. What is the magnitude of the average velocity of the car during this 20.-second interval? [show work] 15-1 Refraction Objective • Recognize situations in which refraction will occur. • Identify which direction light will bend when it passes from once medium to another. • Solve problems using Snell’s law • Homework due: 1. Project 2. Castle learning review corrections 3. 15.1 reading assignment 4. Lab 19: wave on a string • Homework assignment: 1. Castle learning Broken pencil observation • Every object that can be seen is seen only because light from that object travels to our eyes. Refraction of Light Waves • Refraction is the bending of a wave disturbance as it passes at an angle from one medium into another. • When a beam of light approaches a boundary at an angle, it changes direction as it crosses the boundary separating two medium. Light enters the medium at an angle (obliquely) • Since refraction of light occurs when it crosses the boundary, visual distortions often occur. These distortions occur when light changes medium as it travels from the object to our eyes. Atmospheric Refraction • The refraction of light explains – mirages – visibility of the sun after it has actually disappeared below the horizon. Image formed by lenses is refraction – http://www.freezeray.com/flashFiles/eyeDefec ts.htm The Cause of Refraction • Refraction occurs across a boundary between two media is caused by a change in both the speed and wavelength of the wave. • When light enters from denser to less dense (water to air), it speeds up. Since the frequency doesn’t change, the light has a longer wavelength. • When light enters from less dense to denser medium (air to water) it slows down and transforms into a wave with a shorter wavelength. • The only time that a wave can be transmitted across a boundary, change its speed, and still not refract is when the light wave approaches the boundary in a direction which is perpendicular to it. The Ray Model of Light explains refreaction • The ray of wave is constructed in a direction perpendicular to the wave fronts of the light wave, which is the light wave's direction. The idea that the path of light can be represented by a ray is known as the ray model of light. All wave fronts are in phase Conditions of Refraction • A light wave must enter the boundary at an angle (obliquely) in order to bend. A light wave will not undergo refraction if it approaches the boundary in a direction which is perpendicular to it. What we learned • Refraction is the bending of the path of a light wave as it passes from one material into another material. The refraction occurs at the boundary and is caused by a change in the speed and wavelength of the light wave upon crossing the boundary. • The tendency of a ray of light to bend one direction or another is dependent upon whether the light wave speeds up or slows down upon crossing the boundary. The Direction of Bending The speed of a light wave is dependent upon the optical density of the material through which it moves. Light travels faster in less optically dense medium. If a ray of light passes across the boundary from a denser material into a less dense material, such as from water to air, the light ray will bend away from the normal line. If a ray of light passes across the boundary from a less dense material into a denser material, such as from air to water, the light ray will bend towards the normal line. Note: the incident ray and the refracted ray are on the opposite side of the normal line. Class work – today’s date 1. The diagram shows a ray of light passing from air into glass at an angle of incidence of 0°. Which statement best describes the speed and direction of the light ray as it passes into the glass? a. Only speed changes. b. Only direction changes. c. Both speed and direction change. d. Neither speed nor direction changes 2. A change in the speed of a wave as it enters a new medium produces a change in frequency period wavelength phase a. b. c. d. 3. The diagram shows how an observer located at point P on Earth can see the Sun when it is below the observer's horizon. This observation is possible because of the ability of the Earth's atmosphere to a. reflect light b. diffract light c. refract light d. polarize light 4. What happens to the frequency and the speed of an electromagnetic wave as it passes from air into glass? a. The frequency decreases and the speed increases. b. The frequency increases and the speed decreases. c. The frequency remains the same and the speed increases. d. The frequency remains the same and the speed decreases. 5. a. b. c. d. 6. a. b. c. d. Which phenomenon of light accounts for the formation of images by a lens? reflection refraction dispersion Polarization A ray of monochromatic light (f = 5.09 ×1014 hertz) in air incident on flint glass. what happens to the light from the incident ray that is not refracted? It is reflected and converted to mechanical energy. It is reflected, absorbed and energy is decreased. It is all destroyed. It is slowed down, dissolved and reflected. 7. a. b. c. d. Refraction of a wave is caused by a change in the wave's amplitude frequency phase speed 8. The diagram represents wave fronts traveling from medium X into medium Y. All points on any one wave front shown must be a. traveling with the same speed b. traveling in the same medium c. in phase d. superposed 9. a. b. c. d. • The diagram shows a ray of light, R , entering glass from air. Which path is the ray most likely to follow in the glass? A B C D A ray of monochromatic light is incident on an air-sodium chloride boundary. At the boundary, part of the ray is reflected back into the air and part is refracted as it enters the sodium chloride. 10. Compared to the ray's angle of incidence in the sodium chloride, the ray's angle of reflection in the air is _______ (smaller, larger, the same) 11. Compared to the ray's angle of incidence in the sodium chloride, the ray's angle of refraction in the sodium chloride is ___________ (smaller, larger, the same) example 12. What occurs as light travels from alcohol into flint glass? (hint: which material is denser? Check ref. tbl) a. The speed of the light decreases and the ray bends toward the normal. b. The speed of the light decreases and the ray bends away from the normal. c. The speed of the light increases and the ray bands toward the normal. d. The speed of the light increases and the ray bends away from the normal. 4/23 do now • A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 35º with the horizontal, as shown in the diagram. The ball has an initial vertical velocity of 4.9 m/s and a total time of flight of 1.0 second. [Neglect air resistance.] What is the maximum height reached by the ball? [show work] Finish class work from yesterday 15-1 Refraction Objective • Determine the relationship between optical density and index of refraction. • Define dispersion • Solve problems using Snell’s law • Homework assignment: 1. Castle learning Optical Density and Light Speed • An electromagnetic wave (i.e., a light wave) is produced by a vibrating electric charge. As the wave moves through the vacuum of empty space, it travels at a speed of c (3 x 108 m/s). • When light wave moves through a medium that is not vacuum, its speed slows down due to the collision with the particles in the medium. • the speed of the wave depends upon the optical density of that material. The optical density of a medium is not the same as its physical density. Optical Density and the Index of Refraction • One indicator of the optical density of a material is the absolute index of refraction value of the material. • Absolute index of refraction, n, is the ratio of the speed of light in a vacuum, c, to the speed of light in a material medium, v. n=c/v A vacuum is given an n value of 1.0. The absolute index of refraction has no units. The greater the value of n, the denser the medium and the slower light travels in the medium, the shorter the wavelength. The product of the absolute index of refraction of a material and the speed of light in that material is 3.00 x 108 m/s, the speed of light in vacuum. n∙v = c Check your reference table • Absolute indices of refraction: • In what material the light travels slowest? diamond • In what material the light travels fastest? air Index of refraction and ratio of wavelength n1 = c/v1; n2 = c/v2; n2/n1 = v1/v2 Since frequency of the wave does not change v1 = fλ1 and v2 = fλ2 v1/v2 = λ1/λ2 n2/n1 = v1/v2 = λ1/λ2 Dispersion – refraction of white light • The separation of visible light into its different colors is known as dispersion. Wavelength affects index of refraction. Index of red light is the smallest, it bends the least. While index of violet light is greatest, it bends the most. A brief review bending • Refraction is the _______________ of the path of a light wave as it passes across the boundary separating two speed media. Refraction is caused by the change in _________ experienced by a wave when it changes medium. • If a light wave passes from a medium in which it travels slow (relatively speaking) into a medium in which it travels fast, then the light wave will refract away from _____________________ the normal. • On the other hand, if a light wave passes from a medium in which it travels fast (relatively speaking) into a medium in which it travels slow, then the light wave will refract _______________ the normal. towards Question: By how much does light refract when it crosses a boundary? The Angle of Refraction • The amount of refraction of a ray is measured by the angle of refraction. It is the angle between a ray emerging from the interface of two media and the normal to that interface at the point where the ray emerges. • Note: the angle of refraction and the angle of incidence are on the opposite side of the normal. θi is the angle of incidence - the angle which the incident ray makes with the normal line. θr is the angle of refraction - the angle which the refracted ray makes with the normal line. The amount of angle of refraction depends upon the properties of the two media at the interface. Snell’s law • The general relationship governs the refraction of light as it passes from one medium to another of different optical density is known as Snell’s Law n1/n2 = sinθ2/ sinθ1 n1sinθ1 = n2sinθ2 • Angles θ1 and θ2 are the angles of incidence and refraction respectively, and n1 and n2 are the absolute indices of the incident and refractive media, respectively. • If θ1 is zero, θ2 will be zero, which means when light enters perpendicularly to the boundary, it is not changing direction. • Snell’s law can be rearranged in this way sinθ1/sinθ2 = n2/n1 • The ratio n2/n1 is called the relative index of refraction for the two media. Using Snell's Law to Predict An Angle Value • Use Snell's law, a protractor, and the index of refraction values to complete the following diagrams. Measure θi, calculate θr, and draw in the refracted ray with the calculated angle of refraction. 45o 60o 32o 35o Examples 1. A ray of light in air is approaching the boundary with water at an angle of 52 degrees. Determine the angle of refraction of the light ray. 2. A ray of light in air is approaching the a layer of crown glass at an angle of 42.0o. Determine the angle of refraction of the light ray upon entering the crown glass and upon leaving the crown glass. An important concept • When light approaches a layer which has the shape of a parallelogram that is bounded on both sides by the same material, then the angle at which the light enters the material is equal to the angle at which light exits the layer. Class work – today’s date 1. What occurs when light passes from water into flint glass? (hint: which one is denser?) a. Its speed decreases, its wavelength becomes smaller, and its frequency remains the same. b. Its speed decreases, its wavelength becomes smaller, and its frequency increases. c. Its speed increases, its wavelength becomes larger, and its frequency remains the same. d. Its speed increases, its wavelength becomes larger, and its frequency decreases. 2. Which quantity is equivalent to the product of the absolute index of refraction of water and the speed of light in water? (hint: n = c / v) a. wavelength of light in a vacuum b. frequency of light in water c. sine of the angle of incidence d. speed of light in a vacuum 3. If the speed of light in a medium is 2.00 x 108 m/s, what is the absolute index of refraction for the medium? 4. A ray of light (f = 5.09 ×1014 Hz) is incident on the boundary between air and an unknown material X at an angle of incidence of 55°. The absolute index of refraction of material X is 1.66. Determine the speed of this ray of light in material X. 5. A ray of light of frequency 5.09x1014 hertz is incident on a water-air interface. Calculate the speed of the light while in the water. 6. The speed of light (f = 5.09 × 1014 Hz) in a transparent material is 0.75 times its speed in air. What is the absolute index of refraction of the material? 7. Compared to the wavelength of a wave of green light in air, the wavelength of this same wave of green light in Lucite is a. less b. greater c. the same 8. A beam of monochromatic light travels through flint glass, crown glass, Lucite, and water. In which material is the speed of the light beam slowest? 9. The frequency of a ray of light is 5.09 x 1014 Hz. What is the ratio of the speed of this ray in diamond to its speed in zircon? Class work – today’s date 1. The diagram shows a ray of light passing from a medium X into air. What is the absolute index of refraction of medium X? 2. A ray of light (λ = 5.9 × 10-7 meter) traveling in crown glass is incident on a diamond interface at an angle of 30.°. What is the angle of refraction for the light ray? What is the speed of light in glycerol? 3. 4. A ray of light (λ = 5.9 × 10-7 meter) traveling in air is incident on an interface with medium X at an angle of 30.°. The angle of refraction for the light ray in medium X is 12°. What could be the medium X? 5. a. b. c. A ray of light (λ = 5.9 × 10-7 meter) traveling in air is incident on a diamond interface at an angle of 60.°. Draw the reflected ray. Determine the angle of refraction for the light ray. [show work] Draw this refracted ray. 6. A beam of monochromatic light (f = 5.09 × 1014 hertz) passes through parallel sections of glycerol, medium X, and medium Y as shown in the diagram below. What could medium X and medium Y be? a. X could be flint glass and Y could be corn oil. b. X could be corn oil and Y could be flint glass. c. X could be water and Y could be Medium Y has the same index as glycerol. glycerol, so it could be glycerol or d. X could be glycerol and Y could be corn oil. water. Medium x has index higher than glycerol, it could be flint glass 7. A ray of monochromatic light traveling in air enters a rectangular glass block obliquely and strikes a plane mirror at the bottom. Then the ray travels back through the glass and strikes the air-glass interface. Which diagram best represents the path of this light ray? [N represents the normal to the surface.] a c b d 8. In the diagram, a ray of monochromatic light (λ = 5.9 × 10-7 meter) reaches the boundary between medium X and air and follows the path shown. Which medium is most likely medium X? 9. A beam of monochromatic light (λ = 5.9 × 10-7 meter) crosses a boundary from air into Lucite at an angle of incidence of 45°. What is the angle of refraction? 10. A monochromatic ray of light (f = 5.09 ×1014 hertz) traveling in air is incident upon medium A at an angle of 45°. If the angle of refraction is 29°, what could medium A be? 4/24 do now • A child kicks a ball with an initial velocity of 9.8 meters per second at an angle of 30º with the horizontal. [Neglect air resistance.] What is the maximum height reached by the ball? [show work] Finish class work from yesterday 15-1 Refraction Objective • Define critical angle • Determine conditions for total internal reflection • Solve problems using Snell’s law • Homework assignment: 1. Castle learning 2. Quiz on Hooke’s law on Friday 3. Lab 19 is overdue Boundary Behavior Revisited • A light wave, like any wave, is an energy-transport phenomenon. A light wave transports ________ energy from one location to another. • When a light wave strikes a boundary between two distinct transmitted media, a portion of the energy will be _____________ into the new medium and a portion of the energy will be ________________ off the boundary and stay within the reflected original medium. Reflection • _____________ of a light wave involves the bouncing of a refraction light wave off the boundary, while ______________ of a light wave involves the bending of the path of a light wave upon crossing a boundary and entering a new medium. Both reflection and refraction involve a change in direction of a medium wave, but only refraction involves a change in __________. • The fundamental law which governs the reflection of light is called the law of reflection When a light ray reflects off a surface, the angle of incidence is equal to the angle of reflection. • The fundamental law which governs the refraction of light is Snell's Law: n1sinθ1 = n2sinθ2 total internal reflection The complete reflection of light at the boundary of two transparent media; this effect occurs when the angle of incidence exceeds the critical angle. Critical angle • The minimum angle of incidence for which total internal reflection occurs. • Since the maximum possible angle of refraction is 90o, the corresponding incident angle is critical angle. • This particular value for the angle of incidence could be calculated using Snell's Law: n1sinθ1 = n2sinθ2 n1sinθcritical = n2sin90o Example • A laser beam is shining from water into air, what is the critical angle of water? • Given: (ni = 1.33, nr = 1.00, θr = 90o, • Unknown: θi = ? Solve: n1sinθ1 = n2sinθ2 1.33sinθi = (1.00)sin90o θi = 48.7o When the angles of incidence is greater than 48.6o (the critical angle), all of the energy (the total energy) carried by the incident wave to the boundary stays within the water (internal to the original medium) and undergoes reflection off the boundary. Two Requirements for Total Internal Reflection • 1. 2. Total internal reflection (TIR) is the phenomenon which involves the reflection of all the incident light off the boundary. TIR only takes place when both of the following two conditions are met: the light is in the denser medium and approaching the less dense medium. the angle of incidence is greater than the so-called critical angle. TIR and the Sparkle of Diamonds • Relatively speaking, the critical angle for the diamond-air boundary is an extremely small number. This property about the diamond-air boundary plays an important role in the brilliance of a diamond gemstone. Having a small critical angle, light has the tendency to become "trapped" inside of a diamond once it enters. A light ray will typically undergo TIR several times before finally refracting out of the diamond. More examples of TIR A prism in an optical instrument will allow light to undergo TIR whereas a mirror allows light to both reflect and refract. So for a prism, 100 percent of the light is reflected. But for a mirror, only about 95 percent of the light is reflected. Rainbows and bubbles – interference through TIR Ray 1 & 2 interfere Lens Aberrations • Aberrations occurs when light rays enters the lens does not focus on the same point. • Spherical aberrations happens due to the quality of lens. • Chromatic aberrations happens due to different color of light. Class work – today’s date 1. For the following situations, indicate if TIR will happen or not: a. light traveling from water towards air; b. light traveling from air towards water; c. light traveling from water towards crown glass. 2. Calculate the critical angle for the crown glass-air boundary. 3. Calculate the critical angle for the diamond-air boundary. 4. A monochromatic light ray is passing from medium A into medium B. The angle of incidence,θ, is varied by moving the light source, S. When the angle θ equals the critical angle, what is the angle of refraction? 5. Total internal reflection can occur as light waves pass from a. water to air c. Lucite to crown glass b. alcohol to glycerol d. air to crown glass 6. What is the critical angle for the Lucite-air boundary? 7. The absolute index of refraction for a substance is 2.0 for light having a wavelength of 5.9 × 10-7 meter. In this substance, what is the critical angle for light incident on a boundary with air? 8. A ray of light (f = 5.09 ×1014 Hz) is incident on the boundary between air and an unknown material X at an angle of incidence of 55°. The absolute index of refraction of material X is 1.66. Determine the speed of this ray of light in material X. example 9. A ray of monochromatic light is traveling in flint glass. The ray strikes the flint glass-air interface at an angle of incidence greater than the critical angle for flint glass. Which diagram best represents the path of this light ray? A B C D 10. A ray of light (f = 5.09 ×1014 Hz) is incident on the boundary between air and an unknown material X at an angle of incidence of 55°. The absolute index of refraction of material X is 1.50. a. Determine the speed of this ray of light in material X. b. Determine the frequency of this light in material X. c. Determine the wavelength of this light in material X. d. Draw a diagram to indicate the boundary, the normal, the incident ray, the reflected ray and the refracted ray. Lab 36 – finding index of refraction Purpose (5 pt): Determine the index of refraction of an unknown material Material (5 pt): Rectangular prism with unknown index of refraction, Pins, Pencil, Plain paper, Cardboard, Straightedge, Protractor Data section (20 pt): – should contain colomns of measured and calculated data. The rows and columns should be labeled; units should be identified. Work should be shown for one calculation; the work should be labeled and easy to follow. Conclusion/discussion of results (10 pt): Calculate the index of refraction using Snell’s Law. Record your values for n in the data table and calculate the average value of n. 1. Trace the prism on the white paper which is placed on top of the card board. 2. Line up two pins obliquely to the prism, the beam will refract into the prism and then the beam will refract again into the air. 3. Use pins to mark the points of the refracted ray by lining them up with the images of the pins inside the prism. Trace incident ray to the prism and refracted ray out of the prism. Connect two points at the intersections with the prism. Normal Procedure: For each person in the group, trace the prism on a blank sheet of paper. θi Surface 1 θri Surface 2 θi 3. Each person in the group must draw two diagrams to indicate incident rays and refracted rays. 4. Measure the angles of incident and refracted rays. Read the angles to the nearest 1/10th of a degree. 5. Record each person’s data in the group on the data table. Every one in your group should have a data table. 6. Calculate the index of refraction using Snell’s Law. Record your values for n in the data table and calculate the average value of n. Data table trials θi θr n 1 2 3 4 5 6 Average n is nisinθi = nrsinθr ______________________