Lesson 1: Reflection and its ImportanceThe Role of Light to Sight The Line of Sight The Law of Reflection Specular vs. Diffuse Reflection Lesson 4: The Mathematics of RefractionSnell's Law Ray Tracing and Problem-Solving Determination of n Values Lesson 5: Total Internal ReflectionBoundary Behavior Revisited Total Internal Reflection The Critical Angle Lesson 3: Refraction at a BoundaryBoundary Behavior Refraction and Sight The Cause of Refraction Optical Density and Light Speed The Direction of Bending Lesson 2: Image Formation in Plane MirrorsImage Characteristics for Plane Mirrors What Portion of a Mirror is Required to View an Image? Chapter 11: reflection and refraction

Lesson 1: Reflection and its ImportanceThe Role of Light to Sight The Line of Sight The Law of Reflection Specular vs. Diffuse Reflection

The Role of Light to SightWithout light, there would be no sight. The objects which we see can be placed into one of two categories: luminous objects and illuminated objects. Luminous objects are objects which generate their own light. Illuminated objects are objects which are capable of reflecting light to our eyes. The sun is an example of a luminous object, while the moon is an illuminated object.

The Line of Sight The line of sight is a straight line between your eye and the object. In order to view an object, you must sight along a straight line at that object; and when you do, light will come from that object to your eye along the line of sight.

In order to locate the image, two conditions must be satisfied:You must be able to see the image. One of the many rays of light from the object that approach the mirror and must reflect along your line of sight to your eye. Since there is only one image for an object placed in front of a plane mirror, every sight line from different observing places would intersect in a single location. This location of intersection is known as the image location.We use line of sight to determine image location

The image is positioned directly across the mirror along a line which runs perpendicular to the mirror. The distance from the mirror to the object (known as the object distance) is equal to the distance from the mirror to the image (known as the image distance). For all plane mirrors, this equality holds true: Object distance = Image distancefro

The Law of ReflectionThe ray of light approaching the mirror is known as the incident ray (I). The ray of light which leaves the mirror is known as the reflected ray (R). At the point of incidence where the ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror. This line is known as a normal line (N). The normal line divides the angle between the incident ray and the reflected ray into two equal angles. The angle between the incident ray and the normal is known as the angle of incidence (i). The angle between the reflected ray and the normal is known as the angle of reflection (r). The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection. i = r

exampleIdentify which angle is angle of incidence and which angle is angle of reflection.ABCDIncident angle is ___Reflected angle is _____

exampleA ray of light is incident towards a plane mirror at an angle of 30-degrees with the mirror surface. What will be the angle of reflection?

exampleA ray of light is approaching a set of three mirrors as shown in the diagram. The light ray is approaching the first mirror at an angle of 45-degrees with the mirror surface. Trace the path of the light ray as it bounces off the mirror. Continue tracing the ray until it finally exits from the mirror system. How many times will the ray reflect before it finally exits?

Specular vs. Diffuse Reflectionlight reflects off surfaces in a very predictable manner - in accordance with the law of reflection. Once a normal to the surface at the point of incidence is drawn, the angle of incidence can then be determined. The light ray will then reflect in such a manner that the angle of incidence is equal to the angle of reflection. The Law of Reflection is Always Observed (regardless of the orientation of the surface)

Specular reflection: Reflection off of smooth surfaces such as mirrors or a calm body of water. Diffuse reflection: Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway. Each individual ray obeys the laws of reflection.

Why Does a Rough Surface Diffuses A Beam of Light?For each type of reflection, each individual ray follows the law of reflection. However, the roughness of the material means that each individual ray meets a surface which has a different orientation. The normal line at the point of incidence is different for different rays. Subsequently, when the individual rays reflect off the rough surface according to the law of reflection, they scatter in different directions. The result is that the rays of light are incident upon the surface in a concentrated bundle and are diffused upon reflection.

practiceA ray is incident on a plane mirror at 25 degrees (incident angle). Draw a diagram to indicate the The surface of the mirrorThe line of normalThe incident rayThe reflected ray

Lesson 2 - Image Formation in Plane MirrorsWhy is an Image Formed? Image Characteristics in Plane MirrorsRay Diagrams for Plane Mirrors What Portion of a Mirror is Required to View an Image?

Why is an image formed?An image is formed because light gives off from an object in a variety of directions. Some of this light (which we represent by rays) reaches the mirror and reflects off the mirror according to the law of reflection. Each one of these rays of light can be extended backwards behind the mirror where they will all intersect at a point (the image point). Any person who is positioned along the line of one of these reflected rays can sight along the line and view the image - a representation of the object.

Image formation from plane mirrors..\..\RealPlayer Downloads\07PPT03 Image characteristics in a plane mirror.flv

Image characteristics in a plane mirrorAn image has the same size as the object.The image is as far behind the mirror as the object is in front of the mirror.The image has the same orientation as the object.The image is laterally inverted. (left and right reversal)The image is virtual, no actual light meet at the image position. Virtual image can not be captured on a screen.

the lateral inversion (left-right reversal).

exampleIf Suzie stands 3 feet in front of a plane mirror, how far from the person will her image be located?

exampleIf a toddler crawls towards a mirror at a rate of 0.25 m/s, then at what speed will the toddler and the toddler's image approach each other?

Ray diagrams1. Draw the image of the object.2. Pick one extreme on the image of the object and draw the reflected ray that will travel to the eye as it sights at this point.3. Draw the incident ray for light traveling from the corresponding extreme on the object to the mirror. 4. Repeat steps 2 and 3 for another extreme on the object.

Practice draw ray diagram

What Portion of a Mirror is Required?Ray diagrams can be used to determine what portion of a plane mirror must be used in order to view an image. In order to view his image, the man must look as low as his feet, and as high as the tip of his head. The man only needs the portion of mirror extending between points X and Y in order to view his entire image. All other portions of the mirror are useless to the task of this man viewing his own image.to view an image of yourself in a plane mirror, you will need an amount of mirror equal to one-half of your height.

exampleIn the diagram, a light ray leaves a light source and reflects from a plane mirror. At which point does the image of the source appear to be located?A B C D

exampleWhen a ray of light strikes a mirror perpendicular to its surface, the angle of reflection is0 45 60 90

exampleParallel light rays are incident on the surface of a plane mirror. Upon reflection from the mirror, the light rays willconverge diverge be parallel be scattered

exampleA plane mirror produces an image of an object. Compared to the object, the image appearsinverted and the same size reversed and the same size inverted and larger reversed and larger

exampleWhen a student looks into a plane mirror, she sees a virtual image of herself. However, when she looks into a sheet of paper, no such image forms. Which light phenomenon occurs at the surface of the paper?regular reflection diffuse reflection polarization resonance

exampleIn the diagram, a light ray, R, strikes the boundary of air and water. Look at the graph and estimate the approximate degree of the angle of incidence.31 61 119 149

exampleA ray of light strikes a plane mirror at an angle of incidence equal to 45. What is the angle between the incident ray and the reflected ray?

Objective - Refraction at a BoundaryRefraction of Light Waves Refraction and Sight The Cause of Refraction Optical Density and Light Speed The Direction of Bending

Refraction of Light WavesRefraction is a boundary behavior. When a wave reaches the end of one medium and encounters another medium, the transmitted wave undergoes refraction (or bending) if it approaches the boundary at an angle (obliquely). When a beam of light approaches a boundary, it changes direction as it crosses the boundary separating two medium. Light only bends when incident at an angle.

Light enters the medium at an angle (obliquely)

The Ray Model of LightWe will rely on the use of rays to represent the direction in which light is moving. The ray is constructed in a direction perpendicular to the wave fronts of the light wave; this accurately depicts the light wave's direction. In this sense, we are viewing light as behaving as a stream of particles which head in the direction of the ray. The idea that the path of light can be represented by a ray is known as the ray model of light.

Refraction and SightEvery object that can be seen is seen only because light from that object travels to our eyes. When light passes from one medium into a second medium, the light path bends. Refraction takes place. When sighting at an object, light from that object changes media on the way to your eye, a visual distortion is likely to occur. This visual distortion is witnessed if you look at a pencil submerged in a glass half-filled with water.

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.

The refraction of light explains miragesvisibility of the sun after it has actually disappeared below the horizon.Image formed by lenses is refractionhttp://www.freezeray.com/flashFiles/eyeDefects.htm

The Cause of RefractionThe transmission of light across a boundary between two media is accompanied 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 doesnt 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. As long as the light wave changes speed and approaches the boundary at an angle, refraction is observed. Changing speed is the cause of the light wave changes directions at the boundary.

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.

exampleThe 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?Only speed changes. Only direction changes. Both speed and direction change. Neither speed nor direction changes

exampleA change in the speed of a wave as it enters a new medium produces a change infrequency period wavelength phase

exampleThe 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 toreflect light diffract light refract light polarize light

exampleWhich phenomenon of light accounts for the formation of images by a lens?reflection refraction dispersion polarization

exampleBase your answer to the question on the diagram below, which represents 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.

exampleRefraction of a wave is caused by a change in the wave'samplitude frequency phase speed

exampleThe diagram represents wave fronts traveling from medium X into medium Y. All points on any one wave front shown must betraveling with the same speed traveling in the same medium in phase superposed

exampleWhat happens to the frequency and the speed of an electromagnetic wave as it passes from air into glass?The frequency decreases and the speed increases. The frequency increases and the speed decreases. The frequency remains the same and the speed increases. The frequency remains the same and the speed decreases.

The Direction of BendingRefraction 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 speed of a light wave is dependent upon the optical density of the material through which it moves.

Light Traveling from a Fast (less dense) to a Slow (denser) MediumIf a ray of light passes across the boundary from a material in which it travels fast into a material in which travels slower, then 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.

Light Traveling from a Slow (denser) to a Fast (less dense) MediumIf a ray of light passes across the boundary from a material in which it travels slow into a material in which travels faster, then the light ray will bend away from the normal line.

Note: the incident ray and the refracted ray are on the opposite side of the normal line.

exampleThe 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

exampleA ray of monochromatic light is incident on an air-sodium chloride boundary as shown in the diagram below. At the boundary, part of the ray is reflected back into the air and part is refracted as it enters the sodium chloride. 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)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)

exampleWhat occurs as light travels from alcohol into flint glass? (hint: which material is denser? Check ref. tbl)The speed of the light decreases and the ray bends toward the normal. The speed of the light decreases and the ray bends away from the normal. The speed of the light increases and the ray bands toward the normal. The speed of the light increases and the ray bends away from the normal.

Dispersion refraction of white lightThe separation of visible light into its different colors is known as dispersion. Different wavelength corresponds to different colors. Red color bends the least, violet color bends the most.

Optical Density and Light SpeedAn 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. 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.A vacuum is given an n value of 1.0.n = c / vnv = c

Check your reference tableAbsolute indices of refraction:In what material the light travels slowest?

In what material the light travels fastest?

exampleWhat occurs when light passes from water into flint glass? (hint: which one is denser?)Its speed decreases, its wavelength becomes smaller, and its frequency remains the same. Its speed decreases, its wavelength becomes smaller, and its frequency increases. Its speed increases, its wavelength becomes larger, and its frequency remains the same. Its speed increases, its wavelength becomes larger, and its frequency decreases.

exampleWhich 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)wavelength of light in a vacuum frequency of light in water sine of the angle of incidence speed of light in a vacuum

exampleIf the speed of light in a medium is 2.00 x 108 m/s, what is the absolute index of refraction for the medium?

exampleA 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.

exampleA 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.

exampleThe 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?

exampleThe 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?

exampleCompared to the wavelength of a wave of green light in air, the wavelength of this same wave of green light in Lucite isless greater the same

exampleA beam of monochromatic light travels through flint glass, crown glass, Lucite, and water. The speed of the light beam is slowest in flint glass crown glass Lucite water

When Light travel from medium 1 to medium 2n1 = c/v1; n2 = c/v2; n2/n1 = v1/v2Since frequency of the wave does not changev1 = f1 and v2 = f2v1/v2 = 1/2n2/n1 = v1/v2 = 1/2

exampleThe 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?

The Mathematics of RefractionThe Angle of RefractionSnell's Law Ray Tracing and Problem-SolvingDetermination of n Values

A brief reviewRefraction is the _______________ of the path of a light wave as it passes across the boundary separating two 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 _____________________ 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. Question: By how much does light refract when it crosses a boundary?

The Angle of RefractionThe 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.i is the angle of incidence - the angle which the incident ray makes with the normal line.r 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.

Snells lawThe general relationship governs the refraction of light as it passes obliquely from one medium to another of different optical density is known as Snells Law

Angles 1 and 2 are the angles of incidence and refraction respectively, and n1 and n2 are the absolute indices of the incident and refractive media, respectively...\..\RealPlayer Downloads\Snell's Law.flvn1sin1 = n2sin2n1/n2 = sin2/ sin1

Snell's law applies to the refraction of light in any situation, regardless of what the two media are. Snells law can be rearranged in this waysin1/sin2 = n2/n1The 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 i, calculate r, and draw in the refracted ray with the calculated angle of refraction.

exampleA 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.

exampleA 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 conceptWhen 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.

exampleThe diagram shows a ray of light passing from a medium X into air. What is the absolute index of refraction of medium X?

exampleA ray of light ( = 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?

exampleWhat is the speed of light in glycerol?

exampleA ray of light ( = 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?

exampleA ray of light ( = 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.

exampleA 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?X could be flint glass and Y could be corn oil. X could be corn oil and Y could be flint glass. X could be water and Y could be glycerol. X could be glycerol and Y could be water.

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.]example1234

exampleIn the diagram, a ray of monochromatic light ( = 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?diamond flint glass Lucite water

exampleA beam of monochromatic light ( = 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?

Determination of n Values

example

exampleA monochromatic ray of light (f= 5.09 1014hertz) traveling in air is incident upon medium Aat an angle of 45. If the angle of refraction is 29, what could mediumA be?

Total internal reflectionBoundary Behavior Revisited A light wave, like any wave, is an energy-transport phenomenon. A light wave transports ________ from one location to another. When a light wave strikes a boundary between two distinct 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 original medium. _____________ of a light wave involves the bouncing of a 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 wave, but only refraction involves a change in __________. energytransmittedreflectedReflectionrefractionmedium

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: n1sin1 = n2sin2

http://www.upscale.utoronto.ca/PVB/Harrison/Flash/Optics/Refraction/Refraction.htmltotal internal reflection..\..\RealPlayer Downloads\Light refraction.flv

Critical angleThe maximum possible angle of refraction is 90o. There is some specific value for the angle of incidence (we'll call it the critical angle) which yields an angle of refraction of 90o. This particular value for the angle of incidence could be calculated using Snell's Law: n1sin1 = n2sin2n1sincritical = n2sin90o

ExampleA laser beam is shining from water into air, what is the critical angle of water?

Two Requirements for Total Internal ReflectionTotal 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.

exampleFor the following situations, indicate if TIR will happen or not:light traveling from water towards air;light traveling from air towards water;light traveling from water towards crown glass.

exampleCalculate the critical angle for the crown glass-air boundary.

exampleCalculate the critical angle for the diamond-air boundary.

TIR and the Sparkle of DiamondsRelatively 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 TIRA prism will allow light to undergo total internal reflection 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.

exampleA monochromatic light ray is passing from medium A into medium B. The angle of incidence,, is varied by moving the light source, S. When the angle equals the critical angle, the angle of refraction will be0 between 0 and 90 between and 90 90

exampleTotal internal reflection can occur as light waves pass fromwater to air Lucite to crown glass alcohol to glycerol air to crown glass

exampleA ray of monochromatic light is traveling in flint glass. The ray strikes the flint glass-air interface at an angle of incidence greaterthan the critical angle for flint glass. Which diagram best represents the path of this light ray?ACBD

exampleIn the diagram, a ray of monochromatic light ( = 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?diamond flint glass Lucite water

exampleThe diagram represents a beam of monochromatic light ( = 5.9 10-7 meter) traveling from Lucite into air. What is the critical angle for the Lucite-air boundary?

exampleThe 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?

exampleA ray of light (f= 5.09 1014Hz) is incident on the boundary between air and an unknown materialXat an angle of incidence of 55, as shown. The absolute index of refraction of materialXis 1.66. Determine the speed of this ray of light in materialX. [show all work, including equation and substitution with units]