Thanks, Tony!

Physics: Chapter 11 Notes

Chapter 11.1—Refraction of Light

• refraction is the bending of light as it travels, at an angle, from a material with one refractive index to a material with a different refractive index
• a property of light in which the speed of light and its direction of travel change

UNDERSTANDING REFRACTION

• analogy for refraction: when you’re riding a golf cart, and you hit some mud/gravel, the front wheels will suddenly slow down, but the back wheels keep going, causing the golf cart to twist around
• similarly, when light travels from one medium into a different medium, both its speed and direction may change

DESCRIBING REFRACTION

• properties of light which are important in describing refraction:
• light travels in a straight line and at a constant speed as long as the medium it is travelling in is the same
• if light travels from one medium to another (ex: from water to air), the light may refract (bend) causing the direction and speed of light to change
• a wave front is any specific part of a wave (in which you choose to follow)
• a boundary is the surface between the two media in which a light wave is travelling through

FERMAT’S PRINCIPLE

• principle says that when light travels from one point to another, it follows the path that will take the least time
• in a single medium, the path that takes the least time is a straight line
• when travelling from one medium to another, the path that takes the least time in not a straight line
• ex: light travels from air to water—since the light travels faster in air than it does in water, the light will travel a greater distance in air than in water, in order to minimize travel time

DESCRIBING REFRACTION USING RAYS

• there rays:
• incident ray
• reflected ray (will always occur)
• refracted ray—the ray that is bent upon entering a second medium (won’t always occur—T.I.R.)
• the angles:
• angle of incidence
• angle of reflection
• angle of refraction—the angle between the normal and a refracted ray

THE DIRECTION OF THE REFRACTED RAY

• if light travels from a medium in which it travels slower to a medium in which it travels faster, the refracted ray will bend away from the normal
• water to air
• if light travels from a medium in which it travels faster to a medium in which it travels slower, the refracted ray will bend towards the normal
• air to water

INDEX OF REFRACTION

• the index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a given medium
• the equation to calculate the index of refraction is:
• n is the index of refraction
• c is the speed of light in a vacuum
• v is the speed of light in a medium
• how much a light ray refracts is determined by the extent of the change in the speed
• the greater the change in speed (faster), the greater the angle of refraction changes
• the speed of light will always be less than the speed of light in a vacuum (3.0 x 108 m/s)

DISPERSION

• dispersion is the process of separating colours by refraction
• white light includes all the wavelengths of visible light (ROYGBIV)
• in a prism, the light is refracted twice—once when it enters the prism, and once when it leaves the prism
• when the light leaves the prism, it’s separated into a spectrum of colours
• since blue light bends more than red light, blue light travels slower than red light
• in fact, each colour of light travels at a slightly different speed in any medium—only in a vacuum do they all travel at the same speed of light

FERMAT’S PRINCIPLE

• principle says that when light travels from one point to another, it follows the path that will take the least time
• in a single medium, the path that takes the least time is a straight line
• when travelling from one medium to another, the path that takes the least time in not a straight line
• ex: light travels from air to water—since the light travels faster in air than it does in water, the light will travel a greater distance in air than in water, in order to minimize travel time

REPORTING INCICES OF REFRACTION

• even though each colour of light has its own index of refraction, the value of the index of refraction for “light” is the index of refraction for yellow (because it’s the easiest colour the scientists could get)
• when reporting the index of refraction for a gas, the temperature and the pressure of the gas is reported
• in a liquid and solid, the temperature is only reported
• the index of refraction will always be greater than one, because “c” will always be greater than “v” (from the index of refraction equation)
• as the speed of light decreases due to the medium, the index of refraction increases
• there are many indices of refraction for glass—this is because different substances are added in the glass-making process, causing glass to have varying indices (crown glass will have a different index than fused and crystal)
• if you know the index of refraction for a substance, you can calculate the speed of light in that substance as well
• higher index of refraction means a lower speed

Chapter 11.2—Partial Refraction and Total Internal Reflection

• to be able to see an object, the light must travel from the object to your eyes
• ex: if you’re underwater and you can’t see the objects to the far corners of the water, it means that no light from the object is penetrating the surface of the water (it is reflected)

PARTIAL REFLECTION AND REFRACTION

• it is the phenomenon in which some of the light that is travelling from one medium into another is reflected, and some is refracted at the boundary between the media
• example: when you look out a window, you see what’s outside as well as your own reflection
• light is obviously coming in through the window (because you can see objects that are outside), but light is also reflecting off the window because you can see your own reflection
• the amount of reflection compared to the amount of refraction depends on:
• the angle of incidence
• the relative indices of refraction of the two media
• example of light travelling from air into water—if the angle of incidence is nearly zero (light is travelling directly toward the water), most of the light penetrates the surface and very little is reflected; as the angle of incidence increases (sun begins to set/rise), more light is reflected than refracted
• this is why during the day, you see very little reflection of the sunlight since most of the light is penetrating the surface of the water’ however, if the sun is close to the horizon, more of the light is reflected than refracted (because there’s a larger angle of incidence)

REFLECTION AND REFRACTION IN A REARVIEW MIRROR

• the rear-view mirror in most cars has a lever that allows the driver to choose how much light from behind the car will reach the driver’s eyes
• a rear-view mirror is a wedge-shaped and silvered on the back—a lever quickly flips the rear-view mirror from daytime to night time positions
• the angles of incidence, reflection and refraction direct the right amount of light toward the driver’s eyes for both daytime and night time
• light coming from behind the car hits the mirror at a very small angle of incidence—as a result, most of the light is refracted and reaches the silvered back of the mirror where it’s reflected
• during the day, the driver wants to clearly see the traffic that is behind the car; at night, the driver does not want to be blinded by headlights
• the angles of incidence, reflection and refraction direct the right amount of light toward the driver’s eyes for both daytime and night time
• in the daytime, the mirror is positioned so that light has reflected off the back of the mirror and then directed towards the driver’s eyes
• the driver has a clear view of the traffic behind the car (however, if the mirror was left in this position at night, the driver would be blinded by the headlights, because a majority of the light is directed towards the driver)
• in the night time, the angle at which the light penetrates the mirror glass is mostly refracted (like before); however, in this case, only a small amount of reflected light is directed toward the driver’s eyes
• this allows the driver to see the headlights, but at a low intensity
• most of the light penetrates the mirror, refracts, hits the silvered back of the mirror, and is reflected away from the driver’s eyes

LARGER ANGLES OF INCIDENCE

• example: if you’re underwater and looking up at the surface of the water, you will only see light coming from the area directly above you or at a small angle of incidence to the surface of the water
• as the angle of incidence of the light increases, more of the light will reflect off the water, and a smaller amount will refract in order to be visible to you underwater

REFRACTION: WATER TO AIR

• if you were to stand in shallow water at the edge of a clear lake, you would be able to see stones and fish on the bottom
• as you look farther away, objects underwater are more difficult to see (at a great enough distance, you can’t see anything below the surface of the water)

THE CRITICAL ANGLE

• for you to see an object underwater, light must hit the object, reflect off it, and travel to your eyes
• example: light going from water to air—the incident rays will bend away from the normal; as the angle of incidence increases, the angle of refraction increases, but more rapidly
• as the angle if incidence continues to increase, the angle of refraction will eventually reach 90 degrees; at this angle of incidence, the refracted ray lies along the boundary between the two media (no light passes through the second medium (air)
• the critical angle is the angle of incidence that produces an angle of refraction of 90 degrees

TOTAL INTERNAL REFLECTION

• the phenomenon in which incident light is not refracted but is entirely reflected back from the boundary; occurs when light travels from a medium in which its speed is lower to a medium in which its speed is faster
• the size of the critical angle depends on the indices of refraction of the two media
• when the angle of incidence is larger than the critical angle, the angle of refraction can’t get any larger because the refracted ray would no longer be in the second medium
• so at angles of incidence that are greater than the critical angle, no refraction occurs
• all the light is refracted back into the first medium
• total internal reflection can only occur when:
• light travels from a medium in which its speed is lower to a speed in which it is higher
• angle of incidence is greater than critical angle

CHANGING THE DIRECTION OF A LIGHT RAY

• a glass prism can change the direction of light by creating the conditions for total internal reflection
• the critical angle between glass and air is LESS than 45 degrees; therefore, light hitting an inner surface at exactly 45 degrees will be totally reflected inside the glass
• a glass prism that is shaped like an isosceles right triangle (angles are: 45, 45, and 90 degrees)
• when light enters the triangle/prism perpendicular to one of the SHORT sides of the prism, the angle of incidence is 0 (no refraction)
• the light travels straight through the prism to the inside of the long side of the prism
• at the long side of the prism, the angle of incidence is 45 degrees (no refraction—greater than critical angle) so the angle of reflection is also 45 degrees
• the total change in the direction of the ray is 90 degrees (45 degrees x 2 times = 90 degrees)
• if light enters the long side of the prism, there is no angle of refraction
• the light travels straight through the prism to the inside of the short side of the prism, hitting it at 45 degrees, meaning the angle of reflection is 45 degrees also
• the reflected ray then hits the inside of the second short side of the triangle at 45 degrees, meaning the angle of reflection is 45 degrees also
• the total change in direction is 180 degrees (45 degrees x 4 times = 180 degrees)
• when light enters the long side at any angle (not zero degrees),the light will refract, and then reflect off both inner short sides before leaving the prism
• the light is reflected by a total of 180 degrees (back in the same direction it came from)
• after the light reflects off both inner short sides, it will refract in the same angle the light entered the prism

APPLICATIONS OF TOTAL INTERNAL REFLECTION

• binoculars—use total internal reflection (the oath of light in the binoculars is lengthened and moved to the side)
• retroreflectors—they have the ability to change the direction of light by 180 degrees
• appear to be small plastic prisms
• example: the reflectors on the back of a bike
• regardless of the direction that light from headlights hits the reflectors, the light is always directed back to the car so the driver can see the bike
• optical fibres—made of a glass core, which is surrounded by an optical cladding (which is a covering for the glass core)
• the fibre core is made of one type of glass; the cladding is made of another
• the material that makes up the cladding must have a lower reflective index than the core to facilitate total internal reflection (higher reflective index means light travels slower in the material)
• when light enters the end of the fibre in a direction that’s almost parallel to the axis of the fibre, it hits the boundary between the core and cladding at an angle larger than the critical angle (even when the fibre is bent, the light is totally internally reflected along the entire fibre until it reaches the other end)
• individual fibres are somewhat fragile; therefore they are coated for strength and protection—groups of fibres are then bundles together into a cable (depending on their use, the cables vary in length)
• copper wires use to be used to carry information; however, fibre optic cables are rapidly replacing them, because:
• the signals carried by fibre optics aren’t affected by electrical storms as they would be in copper wire cables
• fibre optics can carry many more signals over long distances, losing less energy than copper cables
• fibre optic cables are smaller and lighter than copper cables
• fibre optics has also been used in medicine in the endoscope instrument
• the surgeon inserts the endoscope into a small incision; one bundle of optical fibres in the endoscope caries light into the area where the surgery is needed, while another bundle carries an image of the area back to a monitor—the surgeon watches the monitor while manipulating the instrument to complete the surgery (this technique has made recovery rime shorter, and reduces the possibility of infection)
• doctors also use endoscopes to help diagnose problems—the doctor has fed an endoscope down a patient’s esophagus and can view the inside of the patient’s stomach on a monitor; by being able to see the inside of the stomach and take a tissue sample, the doctor may be able to diagnose any problems (such as an ulcer or cancer

Chapter 11.3—Optical Phenomena in Nature

RAINBOWS

• a rainbow is an arc of colours of the visible spectrum appearing opposite the Sun, caused by reflection, refraction, and dispersion of the Sun’s rays as they pass through raindrops
• the sun must be behind you if you are to see a rainbow; it must also reflect off something for it to return to your eyes
• after a rainstorm, the sky is filled with tiny water droplets for the sunlight to reflect off of
• in a double rainbow, one will have the colours in the order of ROYGBIV while another will have it in VIBGYOR
• a secondary rainbow is caused when sunlight reflects twice inside rain droplets (this explains why the secondary bow is less bright)

FORMATION OF A RAINBOW

• a rainbow forms when sunlight enters a water droplet and refracts, reflects off the inner surface of the droplet, and then refracts again when leaving the droplet
• the two refractions result in the dispersion of the light
• even though red light is the lowest colour leaving the droplet, it is still the top colour in the inner rainbow
• although this may seem to be a contradiction, it’s not—when you see a rainbow, the colours that you see come from different droplets
• because the red light is directed downward more than the other colours of light, you can only see the red light that is coming from droplets higher in the sky

SUNDOGS

• they are bright spots on both sides of the sun
• they are sometimes called mock suns, but they’re technical name is parhelia
• sundogs have something in common with rainbows, but there is a difference—rainbows are a result from sun interacting with water droplets, while sundogs occur when ice crystals in the atmosphere refract light
• the mist stunning sundogs occur on cold, clear, sunny mornings and evenings when there are ice crystals in the air (like cirrus clouds)
• sundogs occur when the sun is low, and near the horizon

THE ILLUSION OF APPARENT DEPTH

• it is the optical effect in which the image of an object appears closer than the object
• an image is formed by reflection in a mirror, and it can also be formed by the refraction of light (as seen through this illusion)
• light rays from the object (in the water) travel to your eyes; the rays have refracted at the surface of the water
• the image of the box is located by tracing the rays backward until they meet
• the image will appear higher and closer to the observer than the object actually is; the bottom of the water body can also be deeper than it appears
• apparent depth is used to describe the level at which the object or the bottom of a water body appears
• example: a fish in a pond is lower in the water than it actually appears to be
• birds however (like the pelican) can account for the illusion of apparent depth, as they’re able to catch fish in the water

SHIMMERINGS AND MIRAGES

• are caused by the refraction of light in an unevenly heated air
• when light travels through air at different temperatures, it refracts because hot air is less dense than cooler air
• because there is no distinct boundary between sections of air at different temperatures, the light does not bend at one specific point—instead if travels along a curved path; since the air is usually moving, the direction and amount of bending is constantly changing also

• a shimmering is the apparent movement of objects in hot air over objects and surfaces
• example of hot objects with hot air: the hood of a car that has been travelling for a long time; the engine of a plane
• when you look through the hot air, objects look and appear as if they’re moving
• a mirage is an optical effect caused by the bending of light rays passing through layers of air that have extremely different temperatures
• a mirage occurs on a much larger scale than shimmering
• most common place to see a mirage is in a very hot desert or on a highway
• the sand or paved surface becomes extremely hot after being in sunlight for several hours—the hot ground heats the air just above it, making the lower layer of air much hotter than the higher air
• when sunlight reaches the hot air near the ground, the sunlight is refracted upwards
• because you are accustomed to assuming that light travels in a straight line, you interpret the origin of the light as being on the ground—an object that appears to be on the ground but is not really, is called a mirage
• the light is actually curving down (because no distinct boundary between cold and hot air) from the sky towards your eyes; however, you assume the light is coming straight ahead on the ground from your eyes(not curved towards the sky)
• although much less common, a mirage can also be caused by the opposite combination of temperatures
• known as temperature inversion—example: sometimes, a wind brings warm air over a very cold ocean
• light from an object on the ground starts to travel upward, but it curves and starts back down when it reaches  warmer air—the light that reaches an observer can even come from beyond the horizon
• when this kind of mirage occurs, you think you are seeing the object in the air
• ex: people have seen ships, icebergs, buildings from a distant city that appear to be sitting above an ocean
• depending on the exact paths of the light through the different temperatures, part of the object sometimes appears to be upside down
• big temperature differences cause light to bend creating images of objects which don’t exist

Handouts

REFRACTION OF LIGHT

• different types of mediums will cause a change in the speed of light (increase or decrease)
• refraction terminology:
• normal
• incident ray
• angle of incidence
• refraction boundary
• refracted ray
• angle of refraction
• if light slows down in medium 2, it bends towards the normal
• angle of incidence is greater than angle of refraction
• if it speeds up in medium 2, if bends away from the normal
• angle of refraction is greater than angle of incidence
• refraction is USUALLY accompanied by reflection (ex: light reflecting and refracting water)
• the slower the speed of light in the medium, the larger the index of refraction
• dispersion is when white light breaks apart as it exits a prism due to different refracted angles of colour light
• red light travels faster than violet light, causing violet light to bend more