Ch24-27_IrwinA

=**__CHAPTERS 24-27: OPTICS & LIGHT__**= toc

**__PC Lesson 1D: Polarization__**
**What is unpolarized light?** A light wave is an electromagnetic wave that travels through the vacuum of outer space. Vibrating electric charges produces light waves. Electromagnetic wave is a transverse wave that has both an electric and a magnetic component. A light wave that is vibrating in more than one plane is unpolarized light. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization. There are four methods of polarizing light: transmission, reflection, refraction, and scattering. When unpolarized light is transmitted through a Polaroid filter, it emerges with one-half the intensity and with vibrations in a single plane; it emerges as polarized light. All of the light can be blocked out if the two polarization axes are perpendicular to each other. Unpolarized light can also undergo polarization by reflection off of nonmetallic surfaces. The extent to which polarization occurs is dependent upon the angle at which the light approaches the surface and upon the material that the surface is made of. Refraction occurs when a beam of light passes from one material into another material. At the surface of the two materials, the path of the beam changes its direction. The refracted beam acquires some degree of polarization. Most often, the polarization occurs in a plane perpendicular to the surface. Polarization also occurs when light is scattered while traveling through a medium. When light strikes the atoms of a material, it will often set the electrons of those atoms into vibration. The vibrating electrons then produce their own electromagnetic wave that is radiated outward in all directions.
 * What is polarized light and polarization?**

__**PC Lesson 2A: The Electromagnetic and Visible Spectra**__
**What are the electromagnetic and visible spectra?** Electromagnetic waves exist with an enormous range of frequencies. This range of frequencies is known as the electromagnetic spectrum. Though electromagnetic waves exist in a vast range of wavelengths, our eyes are sensitive to only a very narrow band, known as the visible light spectrum (ROYGBIV). The separation of visible light into its different colors is known as dispersion. Each color is characteristic of a different wavelength; and different wavelengths of light waves will bend varying amounts upon passage through a prism. When all the wavelengths of the visible light spectrum strike your eye at the same time, white is perceived. Visible light - the mix of ROYGBIV - is referred to as white light. None of the wavelengths would appear as black.

**__PC Lesson 1A-D: Reflection__**
**What is the role of light to sight?** Without light, there wouldn’t be sight. We are able to see because light from an object can move through space and reach our eyes. Luminous objects are objects that generate their own light. Illuminated objects are objects that are capable of reflecting light to our eyes. Humans are illuminated objects like the moon. **What is the law of reflection?** Behavior of light is very predictable. The normal line divides the angle between the incident ray and the reflected ray into two equal angles. (In diagram, I=incident ray, R=reflected ray, Theta=angle of incidence, N=normal line). **What is the difference between specular and diffuse reflection?** The law of reflection is always observed, regardless of the orientation of the surface. Reflection off of smooth surfaces such as mirrors or a calm body of water leads to specular reflection. Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to diffuse reflection.
 * What is the line of sight?** Directing our sight in a specific direction is called the line of sight. In order to view an object, you must sight along a line at that object; and when you do light will come from that object to your eye along the line of sight. Although this light diverges from the object in a variety of directions, your eye only sees the very small diverging cone of rays that is coming towards it. The light ray approaching the mirror is the incident ray. The light ray that reflects off of the mirror and travels to our rye is the reflected ray. The distance from the mirror to the object (object distance) is equal to the distance from the mirror to the image (image distance).



**__PC Lesson 2A-F: Image Formation in Plane Mirrors__**
**Why is an image formed?** In order to see the image of an object in a mirror, you must sight at the image; when you sight at the image, light will come to your eye along that line of sight. Since there is only one image for an object placed in front of a plane mirror, it is reasonable that every sight line would intersect in a single location. This location of intersection is known as the image location. The image location is simply the one location in space where it seems to every observer that the light is diverging from. Regardless of where the observer is located, when the observer sights at the image location, the observer is sighting along a line towards the same location that all other observers are sighting. **What are the characteristics of images?** Type: In the case of plane mirrors, the image is said to be a virtual image. Virtual images are images that are formed in locations where light does not actually reach. Light does not actually pass through the location on the other side of the mirror; it only appears to an observer as though the light is coming from this location. Real images are formed on the same side of the mirror as the object and light passes through the actual image location. They can be projected. Orientations: When an image is reversed it is called left-right reversal. If the image is upside down it is called inverted. It can also be upright (normal). Location: For plane mirrors, the object distance (often represented by the symbol do) is equal to the image distance (often represented by the symbol di). That is the image is the same distance behind the mirror as the object is in front of the mirror. Size: Normal, magnified, vs. reduced. Images formed by plane mirrors are virtual, upright, left-right reversed, the same distance from the mirror as the object's distance, and the same size as the object.**What is a ray diagram?** A ray diagram is a diagram that traces the path that light takes in order for a person to view a point on the image of an object. On the diagram, rays (lines with arrows) are drawn for the incident ray and the r eflected ray. Ray diagrams can be particularly useful for determining and explaining why only a portion of an image or what objects can be seen from a given location.
 * What portion of a mirror is required?** The ray diagram depicts these lines of sight and the complete path of light from his // extremities // to the mirror and to the eye. In other words, to view an image of yourself in a plane mirror, you will need an amount of mirror equal to one-half of your height. The distance that a person stands from the mirror will ** not ** affect the amount of mirror that the person needs to see their image.

**__PC Lessons 3&4: Concave and Convex Mirrors__**
**What are concave mirrors?**Concave mirrors are curved (spherical mirrors). Concave mirrors are on the inside of the sphere. Convex mirrors are on the outside of the sphere. If a concave mirror were a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the center of the mirror. This line is known as the principal axis. The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram below. The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A in the diagram below. The vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is a point known as the focal point ; the focal point is denoted by the letter F in the diagram below. The distance from the vertex to the center of curvature is known as the radius of curvature (represented by R ). The radius of curvature is the radius of the sphere from which the mirror was cut. Finally, the distance from the mirror to the focal point is known as the focal length (represented by f ). Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature. The focal point is the point in space at which light incident towards the mirror and traveling parallel to the principal axis will meet after reflection. **How is an image formed with a concave mirror?**Light always follows the law of reflection, whether the reflection occurs off a curved surface or off a flat surface. Concave mirrors can produce real images and virtual images. The replica is known as the image.**What are the two rules of reflection for concave mirrors?**The image location is the location where all reflected light appears to diverge from. Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.**How do you draw a ray diagram for concave mirrors?** Real images are produced when the object is located a distance greater than one focal length from the mirror. A virtual image is formed if the object is located less than one focal length from the concave mirror. To see why this is so, a ray diagram can be used.**What are the image characteristics for concave mirrors?** LOST: Case 1: center of curve, inverted, reduced, real image Case 2: center of curve, inverted, normal size, real image Case 3: beyond center of curve, inverted, magnified, real image Case 4: no image Case 5: opposite side of the mirror, upright, magnified, virtual image
 * 1) Pick a point on the top of the object and draw two incident rays traveling towards the mirror.
 * 2) Once these incident rays strike the mirror, reflect them according to the two rules of reflection for concave mirrors.
 * 3) Mark the image of the top of the object
 * 4) Repeat the process for the bottom of the object.

The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho). Aberration is a departure from the expected or proper course. Spherical mirrors have an aberration. This defect prohibits the mirror from focusing all the incident light from the same location on an object to a precise point. The defect is most noticeable for light rays striking the outer edges of the mirror. Images from spherical mirrors are often blurry. Any incident ray that strikes the outer edges of the mirror is subject to this //departure from the expected or proper course//. If a cover is placed over the outer edges of the large demonstration mirror. The result is that the image suddenly becomes more clear and focused. When the problematic portion of the mirror is covered so that it can no longer focus (or mis-focus) light, the image appears more focused. A convex mirror is sometimes referred to as a diverging mirror due to the fact that incident light originating from the same point and will reflect off the mirror surface and diverge. The two rules of reflection for convex mirrors are: 1. Pick a point on the top of the object and draw two incident rays traveling towards the mirror. 2. Once these incident rays strike the mirror, reflect them according to the two rules of reflection for convex mirrors. 3. Locate and mark the image of the top of the object. 4. Repeat the process for the bottom of the object. Convex mirrors always produce images that share these characteristics. The location of the object does not affect the characteristics of the image. As the object distance is decreased, the image distance is decreased and the image size is increased. So as an object approaches the mirror, its virtual image on the opposite side of the mirror approaches the mirror as well; and at the same time, the image is becoming larger. L: behind the mirror O: upright S: reduced T: virtual image The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho). In the case of the image distance, a negative value always indicates the existence of a virtual image located behind the mirror. In the case of the image height, a positive value indicates an upright image.
 * What are the mirror & magnification equations for concave mirrors?**
 * What is spherical aberration?**
 * How are images created on convex mirrors?**
 * Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect in such a manner that its extension will pass through the focal point.
 * Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis.
 * How do you draw ray diagrams for convex mirrors?**
 * If the object is a vertical line, then the image is also a vertical line.
 * What are the image characteristics for convex mirrors?**
 * What are the mirror & magnification equations for convex mirrors?**

__**PC Lesson 2: Color & Vision**__
An approximate range of wavelengths is associated with the various perceived colors within the spectrum. Light that enters the eye through the pupil ultimately strikes the inside surface of the eye, the retina. The retina is lined with a variety of light sensing cells known as rods and cones.When light of a given wavelength enters the eye and strikes the cones of the retina, a chemical reaction is activated that results in an electrical impulse being sent along nerves to the brain. It is believed that there are three kinds of cones, each sensitive to its own range of wavelengths within the visible light spectrum. These three kinds of cones are referred to as red cones, green cones, and blue cones because of their respective sensitivity to the wavelengths of light that are associated with red, green and blue. The following is a cone sensitivity curve. **__What are light absorption, reflection, and transmission?__**Objects have a tendency to selectively absorb, reflect or transmit light certain frequencies. The manner in which visible light interacts with an object is dependent upon the frequency of the light and the nature of the atoms of the object. The selective absorption of light by a particular material occurs because the selected frequency of the light wave matches the frequency at which electrons in the atoms of that material vibrate. Reflection and transmission of light waves occur because the frequencies of the light waves do not match the natural frequencies of vibration of the objects. If the object is transparent, then the vibrations of the electrons are passed on to neighboring atoms through the bulk of the material and reemitted on the opposite side of the object. If the object is opaque, then the vibrations of the electrons are not passed from atom to atom through the bulk of the material. The electrons of atoms on the material's surface vibrate for short periods of time and then reemit the energy as a reflected light wave. If an object absorbs all frequencies of visible light except for the one associated with a particular color, then the object will appear that color. Chemicals that are capable of selectively absorbing one or more frequency of white light are called pigments.**What is color addition?**Any three colors (or frequencies) of light that produce white light when combined with the correct intensity are called primary colors of light. The most common set of primary colors is red (R), green (G) and blue (B). (R+G+B=W) Yellow, magenta, cyan are secondary colors of light. **What is color subtraction?**The ultimate color appearance of an object is determined by beginning with a single color or mixture of colors and identifying which color or colors of light are subtracted from the original set. (W-B=R+G+B-B=R+G=Y) A pigment that absorbs a single frequency is known as a pure pigment. The color of light absorbed by a pigment is merely the complementary color of that pigment. Thus, pure blue pigments absorb yellow light (which can be thought of as a combination of red and green light). ** How are blue skies and red sunsets created? **Atmospheric nitrogen and oxygen scatter violet light most easily. So as white light from the sun passes through our atmosphere, the high frequencies (BIV) become scattered by atmospheric particles while the lower frequencies (ROY) are most likely to pass through the atmosphere. This scattering of the higher frequencies of light illuminates the skies with light on the BIV end of the visible spectrum. Our eyes are more sensitive to light with blue frequencies. Thus, we view the skies as being blue in color. As the path that sunlight takes through our atmosphere increases in length, ROYGBIV encounters more and more atmospheric particles. This results in the scattering of greater and greater amounts of yellow light. During sunset hours, the light passing through our atmosphere to our eyes tends to be most concentrated with red and orange frequencies of light. For this reason, the sunsets have a reddish-orange hue.
 * For Lesson 2A The Electromagnetic and Visible Spectra … see previous summary above**
 * What is the eye's response to visible light?**

**__PC Lesson 1A-F: Refraction at a Boundary__**
**Refraction at a Boundary** A wave will undergo certain behaviors when it encounters the end of the medium. In a wave rope, a portion of the energy carried by the incident pulse is reflected and returns towards the left end of the thin rope. The disturbance that returns to the left after bouncing off the boundary is known as the reflected pulse. A portion of the energy carried by the incident pulse is transmitted into the thick rope. The disturbance that continues moving to the right is known as the transmitted pulse. When passing from air into glass, both the speed and the wavelength decrease. The light is observed to change directions as it crosses the boundary separating the air and the glass. This bending of the path of light is known as refraction. Once the wavefront has passed across the boundary, it travels in a straight line. Refraction is called a boundary behavior. 

**Refraction and Sight** Directing of our sight in a specific direction is sometimes referred to as the line of sight. As light travels through a given medium, it travels in a straight line. However, when light passes from one medium into a second medium, the light path bends. The refraction occurs only at the boundary. If when sighting at an object, light from that object changes media on the way to your eye, a visual distortion is likely to occur.  There are two conditions that are required in order to observe the change in direction of the path of the students: 1 the students must change speed when crossing the boundary 2. the students must approach the boundary at an angle; refraction will not occur when they approach the boundary //head-on// (i.e., heading perpendicular to it). Light wave will not undergo refraction if it approaches the boundary in a direction that is perpendicular to it.  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). The speed of the wave depends upon the ** optical density ** of that material. The optical density of a material relates to the sluggish tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance. The more optically dense that a material is, the slower that a wave will move through the material. One indicator of the optical density of a material is the ** index of refraction value ** (n) of the material. 
 * The Cause of Refraction **
 * Optical Density and Light Speed **

If 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. If a ray of light passes across the boundary from a material in which it travels slowly into a material in which travels faster, then the light ray will bend away from the normal line. There is no ultimate change in the direction that the light is traveling if the two sides of the glass through which the light enters and exits are parallel to each other and if the medium surrounding the glass on the side through which the light enters and exits are the same. Least time principle: Of all the possible paths that light might take to get from one point to another, it always takes the path that requires the least amount of time.
 * The Direction of Bending **

**__PC Lesson 2A-D: The Mathematics of Refraction__**
**The Angle of Refraction** Refraction is the bending of the path of a light wave as it passes across the boundary separating two media. It is caused by the change in speed experienced by a wave when it changes medium. If a light wave passes from slow medium into a fast medium, then the light would refract away from the normal. If a light wave passes from a fast medium into a slow medium, then the light will refract towards the normal. Wherever the light speed changes most, the refraction is greatest. **Snell's Law**  Snell's Law equation is valued for its predictive ability. When light approaches a layer that 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. **Determination of n Values** Snell's law can be used to identify an unknown material, by finding its index of refraction.
 * Ray Tracing and Problem-Solving **

**__PC Lesson 3&4: Total Internal Reflection & interesting Refraction Phenomena__**
At the point of incidence (the point where the incident ray strikes the boundary), a normal line is drawn. The normal line is always drawn perpendicular to the surface at the point of incidence. The normal line creates a variety of angles with the light rays; these angles are important and are given special names. The angle between the incident ray and the normal is the angle of incidence. The angle between the reflected ray and the normal is the angle of reflection. And the angle between the refracted ray and the normal is the angle of refraction. When a light ray reflects off a surface, the angle of incidence is equal to the angle of reflection. **Total Internal Reflection** <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;">Total internal reflection is the reflection of the total amount of incident light at the boundary between two media. TIR only takes place when the light is in the denser medium and approaching the less dense medium and the angle of incidence is greater than the so-called critical angle. Total internal reflection only occurs with angles larger than the critical angle. The separation of visible light into its different colors is known as dispersion. The angle of deviation is the angle made between the incident ray of light entering the first face of the prism and the refracted ray that emerges from the second face of the prism. There are countless paths by which light rays from the sun can pass through a drop. Each path is characterized by this bending towards and away from the normal. One path of great significance in the discussion of rainbows is the path in which light refracts into the droplet, internally reflects, and then refracts out of the droplet. With nonparallel sides, the refraction of light at two boundaries of the droplet results in the dispersion of light into a spectrum of colors. The shorter wavelength blue and violet light refract a slightly greater amount than the longer wavelength red light. Since the boundaries are not parallel to each other, the double refraction results in a distinct separation of the sunlight into its component colors. A mirage is an optical phenomenon that creates the illusion of water and results from the refraction of light through a non-uniform medium.This is commonly seen when there is water on the road.
 * Boundary Behavior Revisited**
 * Dispersion of Light By Prisms**
 * Rainbow Formation**
 * Mirages**

**__PC Lesson 5: Image Formation By Lenses__**
In order to view an object, you must sight along a line at that object; and when you do light will come from that object to your eye along the line of sight. Image location is a location in space where all the reflected light appears to come from. Virtual images are images that are formed in locations where light does not actually meet. Case 1:inverted, real, reduced, between F and 2F on other side of lens Case 2: inverted, real, normal size, at 2F on other side of lens Case 3: inverted, real, enlarged, beyond 2F on other side of lens Case 4: No image Case 5: upright, virtual, enlarged, between F and 2F on same side of lens
 * Lens:** piece of transparent material that refracts light rays to form an image
 * Principal Axis**: horizontal axis where focus is located
 * Converging Lens:** converges rays of light that are traveling parallel to the principal axis
 * Diverging Lens:** diverges rays of light that are parallel to the principle axis
 * Vertical Axis:** imaginary line that bisects the symmetrical lens into halves
 * Focal Point:** intersection point, lenses have two focal points
 * Focal Length:** the distance from the mirror to the focal point
 * 2F Point:** point on the principal axis that is twice as far from the vertical axis as the focal point
 * Refraction Rules for Converging Lens:**
 * 1) Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.
 * 2) Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.
 * 3) Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
 * Refraction Rules for a Diverging Lens**
 * 1) Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel //in line with// the focal point (i.e., in a direction such that its extension will pass through the focal point).
 * 2) Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
 * 3) An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.

**__PC Lesson 6: The Eye__**
Most of the refraction occurs at the cornea. The cornea is the outer membrane of the eyeball that has an index of refraction of 1.38. The index of refraction of the cornea is significantly greater than the index of refraction of the surrounding air. This difference in optical density between the air the corneal material combined with the fact that the cornea has the shape of a converging lens is what explains the ability of the cornea to do most of the refracting of incoming light rays. The crystalline lens is able to alter its shape due to the action of the ciliary muscles. This serves to induce small alterations in the amount of corneal bulge as well as to fine-tune some of the additional refraction that occurs as light passes through the lens material. The ability of the eye to adjust its focal length is known as **accommodation**. Farsightedness or hyperopia is the inability of the eye to focus on nearby objects. The farsighted eye has no difficulty viewing distant objects. Nearsightedness or myopia is the inability of the eye to focus on distant objects. The nearsighted eye has no difficulty viewing nearby objects. But the ability to view distant objects requires that the light be refracted less.
 * Cornea-** thin membrane that has an index of refraction of approximately 1.38, has a dual purpose of protecting the eye and refracting light as it enters the eye
 * Pupil**- merely an opening, the light that the pupil allows to enter the eye is absorbed to the retina and does not exit the eye
 * Iris-** colored part of the eye, diaphragm that is capable of stretching and reducing size of the opening
 * Crystalline Lens-** made of layers of a fibrous material that has an index of refraction of 1.4, able to change its sjhape and serves to fine-tune the vision process
 * Ciliary Muscles-** relax and contract in order to change the shape of the lens, assist the eye in the critical task of producing an image on the back of the eyeball
 * Retina-** inner surface of the eyes, contains rods and cones that detect the intensity and frequency of incoming light
 * Optic Nerve-** network of nerve cells bundled together on the very back of the eyeball