CH24-27_Optics

=CH24: Optics=

Guiding Questions
toc

Lesson 1D
What is polarization?
 * Polarized light waves are light waves in which the vibrations and movement of the wave are on a single pane. Unpolarized light can move and vibrate along multiple planes (up and down + left and right), but can be forced into moving along a single plane by a process of polarization. This restricting of the light's movement can be done in multiple ways.
 * Polarization by Transmission can be done with a Polaroid filter, which limits the direction of movement of light rays which pass through, as seen in the image:
 * [[image:u12l1e2.gif]]
 * Polarization by Reflection is done when light reflects off of a surface, the reflected light is polarized.
 * [[image:u12l1e5.gif]]
 * Polarization by Refraction occurs when light is refracted upon entering the surface of a material.
 * [[image:u12l1e6.gif]]
 * Polarization by Scattering occurs when light scatters when traveling through a medium.

Lesson 2A
What is the electromagnetic and visible spectra?
 * The list of electromagnetic waves can be described by their frequencies, and wavelengths. The list of electromagnetic waves can be placed in what is called the electromagnetic spectra. This spectra lists the waves based upon their frequencies AND wavelengths at the same time, as they are indirectly related to one another. In most cases, the electromagnetic spectrum is in order of long wavelength and low frequency to small wavelength and high frequency from left to right.
 * [[image:u12l2a1.gif]]
 * The visible spectra is the same as the electromagnetic spectra except that it is only for visible light. The visible spectra can be best described as the different colors of the rainbow, as the color waves are in the order of the rainbow Red Orange Yellow Green Blue Indigo Violet. The visible spectra is the same as the electromagnetic spectra in that it goes from large wavelength to small wavelength from left to right.

=CH25: Mirrors and Lenses=

Lesson 1

 * __What is the role of Light to Sight?__**
 * Without light, there would be no sight! Light travels from the object to the eye, making it capable of being seen. There are two types of objects, luminous objects- which give off there own light, and illuminated objects which reflect other light towards the eye. With the lights off, a laser pointer, and a mirror, the following can be demonstrated:
 * [[image:u13l1a2.gif]]


 * __What is the Line of Sight?__**
 * The Line of sight is the straight line path of light that reaches your eye. When an object is within the Line of sight, it has a straight line path for light to shine from the object to the eye and can be seen. The ray of light that travels from the object to the eye is called the incident ray. When this incident ray reflects from a surface such as a mirror, it creates a reflection in the direction of the ray of light, and becomes the Reflected Ray. [[image:u13l1b2.gif width="285" height="236"]] Notice that the image is on the other side of the mirror from the object and eye, and this is because the eye sees light as as straight line, so it appears to continue through the surface into the mirror. For a plane mirror such as this one, the objects distance from the mirror is the same as the image's distance from the mirror on the other side.


 * __What is the Law of Reflection?__**
 * When light is reflected off of a surface, the incident ray hits the mirror at an angle relative to the mirror's normal (line perpendicular to the mirror), and the reflected ray shines away from the mirror at the same angle relative to the normal of the mirror. This can be written as Øi=Ør, where Øi and Ør can be seen in the diagram:
 * [[image:Screen_shot_2012-01-21_at_11.22.48_AM.png]]
 * This law better allows us to find the location of an image as well as the object and image distances when an object is reflected.

> Specular reflection is when light reflects off of smooth surfaces, such as mirrors, while diffuse reflection is when light reflects from uneven and jagged surfaces, such as an asphalt roadway. When light approaches a surface to reflect from it, it travels in parallel rays of incidence, and reflect with respect to the normal line of the surface where it makes contact. For a smooth surface of specular reflection, the rays all reflect in the same direction and remain parallel, but with rough surfaces each ray reflects relative to where they make contact, and often reflect in all different directions, scattering the reflected rays. As a result, Specular Reflection creates a visible and clear reflection image, while the rough surface and Diffuse Reflection creates a blurry image that can not be made out into any clear image. Diffuse Reflection can be seen most commonly as blue along a road in the distance. The light reflects to create an image, but because it is diffuse reflection it can not be made out into a clear image.
 * __What is the difference between Specular and Diffuse Reflection?__**

Lesson 2

 * __Why is an image formed?__**
 * To see the image of an object in a mirror, you must look at the image; when you see the image, light will come to your eye along that line of sight. Because of this the image location is where the viewers are looking when seeing the image, and in the case of a plane mirror it is behind the mirror. The image location is the one location in space where it seems to every observer that the light is coming from. Because of the law of reflection we can find where this is on a diagram simply by knowing where the object and viewers are, assuming that it is a plane mirror.
 * [[image:u13l2a2.gif]]


 * __What are the image characteristics for Plane Mirrors?__**
 * The first image characteristic is the image location, which is the location in space where all of the reflected light of the object are perceived to be coming from. Then there are real and virtual images, For plane mirrors, the image always appears to be beyond the mirror and behind it, and because the image could not be actually located there, the image is virtual. The next feature is the left-right reversal of the image. For an object that is symmetrical this is hard to notice, but when a person raises just their left hand while in front of a plane mirror, the image will appear to raise their right hand. Letters would also be seen in reverse order and backwards. The next feature is that the image will be upright, rather than inverted. This means that the image will appear right-side up rather than up-side down. And the last noticeable feature of the image is that the magnification of the image will be the same size as the object.
 * [[image:u13l2b2.gif]]


 * __What are Ray Diagrams for Plane Mirrors?__**
 * A ray diagram is a diagram that traces the path that light takes to get from the object to the viewer. On the diagram rays are drawn as arrows for incident, reflected, and refracted rays to show the complete path of the light. There are a few steps to making the ray diagram, the first being to draw the object, mirror, and viewer. Then you draw the image location, and draw a light ray arrow from one end of the image to the viewer. At the point where this light ray intersects the mirror, draw an arrow to the object at the same edge as the edge drawn of the image. Then repeat the process for the opposite end of the image and you have made a ray diagram. Ray diagrams can be used to see what a viewer can see through a mirror of certain length with ray diagrams..
 * [[image:u13l2c5.gif]]


 * __What portion of a Mirror is required to View an Image?__**
 * Ray diagrams can be used to determine what portion of a mirror is needed to view the full image. In the case of a person wanting to see himself in a mirror, we draw the image of the man, and draw lines from the man's eyes to the top of the head of the image, as well as a line from his eye's to the feet of the image. From this ray diagram we can determine that the man requires a mirror that is 1/2 his height in the right location, regardless of how close or far away he is from the mirror.
 * [[image:u13l2d2.gif]]


 * __What are Right Angle Mirrors?__**
 * Right Angle Mirrors are two plane mirrors placed at a right angle to one another and touching. Such a system of mirrors will create three images, one image by each of the two mirrors, and one created at the crease of the two mirrors. The two images creates by just one of the mirrors are called the primary images, and are the same as looking into any plane mirror. The third image formed at the crease is a secondary image, and is unique because it does not have the left-right reversal that the primary images have. The primary images are formed, as expected, on the other side of each plane mirror, while the secondary image appears on the other side of the crease and the same distance away. Also if we look closely at the ray diagram for the third image, we can see why the left-right reversal does not appear here. To form this image, the light from the object reflects off of one mirror onto the other mirror, and then reflects again to the eye. Because of the double reflection, the left and right are correct.
 * [[image:u13l2e3.gif]]


 * __What are Other Multiple Mirror Systems?__**
 * For multiple mirror systems, we must look at two mirrors at different angles from one another. For one mirror we get one image, for 90º we get 3 images, for 60º, however, we get more than 3 images, and for 2 parallel mirrors we get an infinite amount. When we looked at 90º mirrors we saw that a third reflection could be created when light reflected off one mirror into the other and then into the eye, and the same is true for 60º. Another possibility for 60º, however, is for there to be three reflections for the light to reach the eye. Therefor there are more images created. And for parallel mirrors there are an infinite number of reflections because one mirror can reflect directly to the other and back without changing the angle of incidence.
 * [[image:u13l2f2.gif]]

Lesson 3

 * __What is the anatomy of a Curved Mirror?__**
 * Mirrors that are curved into a spherical shape are called spherical mirrors, and there are two types of such mirrors. Concave mirrors are one whose center and focal point are on the same side of the mirror as the object, as if the object were within the spherical aberration. Convex mirrors are one whose center and focal point are on the opposite side of the mirror as the object, as if the object were outside of the spherical aberration. Important terms are the PRINCIPAL AXIS-(the axis that runs parallel to the mirror, through its vertex, focal point, and center of curvature), FOCAL POINT-(point where the light rays are directed towards when they travel into the mirror in a path parallel to the principal axis, this point is located halfway between the center of curvature and the vertex), CENTER OF CURVATURE- (The center of the sphere that would be made by this mirror if it continued around), RADIUS OF CURAVTURE-(distance from the vertex to the center of curvature), VERTEX-(point where the principal axis meets the mirror), and FOCAL LENGTH-(distance from vertex to focal point)
 * [[image:u13l3a2.gif]]


 * __What is the reflection of light and the Image Formation?__**
 * The reflection of light ALWAYS follows the law of reflection, and the angle of incidence equals the angle of reflection. When a ray diagram is drawn with this knowledge we find that the rays from an object to the mirror all reflect through the same point, which is our image location. For concave mirrors the image location is real and it is an inverted image.
 * [[image:u13l3b2.gif]]


 * __What are the two rules 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.
 * [[image:u13l3c1.gif]]


 * __What are ray diagrams for Concave Mirrors?__**
 * Pick a point on the top of the object and draw two incident rays traveling towards the mirror.
 * Once these incident rays strike the mirror, reflect them according to the two rules of reflection for concave mirrors.
 * Mark the image of the top of the object
 * Repeat the process for the bottom of the object.
 * 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 Image Characteristics for Concave Mirrors?__**
 * 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
 * [[image:u13l3e1.gif]]


 * __What is the mirror equation for Concave Mirrors?__**
 * f is + if the mirror is a concave mirror
 * f is - if the mirror is a convex mirror
 * di is + if the image is a real image and located on the object's side of the mirror.
 * di is - if the image is a virtual image and located behind the mirror.
 * hi is + if the image is an upright image (and therefore, also virtual)
 * hi is - if the image an inverted image (and therefore, also real)
 * [[image:u13l3e1.gif]]


 * __What is Spherical Aberration?__**
 * **Aberration** - a departure from the expected or proper course.
 * Spherical mirrors have an aberration. There is an intrinsic defect with any mirror that takes on the shape of a sphere. 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. Spherical aberration is most commonly corrected by use of a mirror with a different shape. Usually, a parabolic mirror is substituted for a spherical mirror. The outer edges of a parabolic mirror have a significantly different shape than that of a spherical mirror. Parabolic mirrors create sharp, clear images that lack the blurriness which is common to those images produced by spherical mirrors.

Lesson 4
__What is the Reflection and Image Formation for Convex Mirrors?__
 * Image formation is the same for Convex mirrors as concave mirrors, where the law of reflection applies to create the ray of reflection. For Convex mirrors, however, the image is going to be virtual and appear behind the mirror. As a result, we must extend the reflected ray into the mirror in order to find the image location.
 * [[image:u13l4a3.gif]]

__What are Ray Diagrams for Convex Mirrors?__
 * Pick a point on the top of the object and draw two incident rays traveling towards the mirror.
 * Once these incident rays strike the mirror, reflect them according to the two rules of reflection for convex mirrors.
 * Locate and mark the image of the top of the object.
 * Repeat the process for the bottom of the object.
 * [[image:u13l4b4.gif]]

__**What are Image Characteristics for Convex Mirrors?**__ >
 * ** located behind the convex mirror
 * a virtual image
 * an upright image
 * reduced in size (i.e., smaller than the object)
 * [[image:u13l4c2.gif]]

__**What is The Mirror Equation for Convex Mirrors?**__
 * Same as with concave mirrors. The only difference is that the focal length is going to be negative, not positive.

Lesson 2: Color and Vision
__What are The Electromagnetic and Visible Spectra?__
 * The list of electromagnetic waves can be described by their frequencies, and wavelengths. The list of electromagnetic waves can be placed in what is called the electromagnetic spectra. This spectra lists the waves based upon their frequencies AND wavelengths at the same time, as they are indirectly related to one another. In most cases, the electromagnetic spectrum is in order of long wavelength and low frequency to small wavelength and high frequency from left to right.
 * [[image:u12l2a1.gif]]
 * The visible spectra is the same as the electromagnetic spectra except that it is only for visible light. The visible spectra can be best described as the different colors of the rainbow, as the color waves are in the order of the rainbow Red Orange Yellow Green Blue Indigo Violet. The visible spectra is the same as the electromagnetic spectra in that it goes from large wavelength to small wavelength from left to right.

What is Visible Light and the Eye's Response?
 * 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, blue cones, green cones, and red cones.
 * [[image:u12l2b1.gif]] [[image:u12l2b2.gif]]

What is the Light Absorption, Reflection, and Transmission?
 * 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. When light waves of these frequencies strike an object, the electrons in the atoms of the object begin vibrating. But instead of vibrating in resonance at a large amplitude, the electrons vibrate for brief periods of time with small amplitudes of vibration; then the energy is reemitted as a light wave. 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. Such frequencies of light waves are said to be transmitted If the object is opaque, then the vibrations of the electrons are not passed from atom to atom through the bulk of the material. Rather 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. Such frequencies of light are said to be reflected.

What is Color Addition
 * When primary colors are both at the same point or location, they add to each other, making a final combination of the two colors. The primary colors are Red, Blue, and Green, and adding any combination of them can make any color imaginable.
 * [[image:u12l2d1.gif]]

What is Color Subtraction
 * Color subtraction occurs when a color from a ray of light is lost, which occurs when light is absorbed when reflecting off of a surface. When this color is absorbed, it can no longer be seen by the eye, and the object appears to be a different color than what it really is.
 * [[image:u12l2e1.gif]]


 * What causes Blue Skies and Red Sunsets**
 * 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.

=CH_26- Refraction=

Lesson1
What is Refraction's Boundary Behavior?
 * __Reflected Pulse-__ A disturbance that returns in the opposite after bouncing of a boundary
 * __Transmitted Pulse-__ A disturbance that continues through the boundary into the new medium
 * __Refraction-__ the bending of the path of light (is a boundary behavior)

What is Refraction and Sight?
 * Distortion is an effect of the refraction of light, and the eye-brain interaction cannot account for the refraction of light. This causes an object being refracted to appear distorted or out of position compared to what is expected.
 * Light rays from the submerged portion of the pencil will intersect in a different location than light rays from the portion of the pencil that extends above the surface of the water. For this reason, the submerged portion of the pencil appears to be in a different location than the portion of the pencil that extends above the water.
 * [[image:u14l1b2.gif]]

What is The Cause of Refraction?
 * Refraction occurs as light passes across the boundary between two different medium. This transmission of light across a boundary between two different medium causes a change in wavelength and velocity and the light ray changes direction. The only time the light does not change directions when passing this boundary is when it approaches the boundary from a perpendicular path.
 * [[image:u14l1c3.gif]]

What is Optical Density and Light Speed? > __Index of Refraction Value-__ the number of times slower that a light wave would be in that material than it is in a vacuum
 * __Optical Density-__ 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
 * [[image:u14l1d1.gif]]

What is the Direction of Bending? >
 * The direction of bending of refracted light depends on the change in n of the 1st and 2nd medium that the light travels through. When the change in n is from high to low the light bends toward the normal line, when the change in n is from low to high the light bends away from the normal line.
 * Fast to slow: Slow to fast:

Lesson 2
What is The Angle of Refraction?
 * Refraction occurs when light passes through a boundary from one medium to a different one. The angle of the light meeting with the surface of the second medium is called the angle of incidence, and the angle that the light refracts is called the angle of refraction. These angles are both in respect to the normal axis. The angle of refraction is determined by the index of refraction of both mediums as well as the angle of incidence.

What is Snell's Law?
 * Sine's Law is a relationship found between the index of refraction of the two mediums, and the sin of the angle of incidence and the sin of the angle of refraction. The relationship was found by measuring the angle of incidence and each of the angles of refraction, and making a graph of the sin of these angles. The slope of this graph could be used to find the index of refraction, and an equation was written as: n1*sinØi=n2*sinØr.
 * [[image:u14l2b2.gif]]

What is Ray Tracing and Problem-Solving?
 * To draw a ray diagram we start by creating the normal to the border that the light will pass. Then, with respect to the normal axis, we draw the ray of incidence which approaches at an angle of incidence if it is given. Then on the other side of the border we draw the refracted ray at the angle of refraction if it is given.
 * To solve for any piece of information we don't know in the problem we use Snell's Law, which is the equation n 1 *sinØ i =n 2 *sinØ r.
 * [[image:u14l2c12.gif]]

How do You Determine N Values?
 * N values are different for each medium that light travels in. There are some n values that we know (air = 1) and we can use to find the n values that we do not know. If we measure the angle of incidence and angle of refraction for a ray of light shining through an object of unknown n, we can use Snell's Law to solve for n for that object. (n 1 *sinØ i =n 2 *sinØ r )

Lesson 3
What is boundary behavior?
 * When light reaches the end of a medium it does not simply stop, but does other things. When the light reaches the border between two different medium it will reflect or refract. It is important to remember that reflecting will not change the medium the light travels on, only refracting. When we draw the ray diagram, we notice that at the point of incidence, the light both reflects and refracts. The light that reflects reflects at the angle of reflection, which is equal to the angle of incidence, and the light that refracts refracts at the angle of refraction, which can be found using the equation for Snell's Law.

What is Total Internal Reflection?
 * Total Internal Reflection is the reflection of the total amount of incident light at the boundary between two media, meaning that all of the light is reflected and none of it is refracted. This occurs when the angle of refraction is greater than 90º and in the same medium as the incidence ray. When this happens, which depends simply on the angle of incidence, none of the light is refracted and it is all reflected instead. The maximum angle of incidence at which the light refracts at 90º is called the critical angle.
 * the light is in the more dense medium and approaching the less dense medium.
 * the angle of incidence is greater than the so-called critical angle.
 * This principle is how fiber optics work, as light signals are internally reflected along the wires or pipes from the company to the customer. This causes there to be no heat in the wires and conserves energy when total internal reflection is properly achieved.
 * [[image:u14l3b5.gif]]

What is the Critical Angle?
 * The critical angle is the angle of incidence that will cause an angle of refraction to be 90º. Any angle of incidence greater than the critical angle will cause total internal reflection. Snell's law can be used where the angle of incidence is the critical angle to solve for the critical angle.
 * [[image:Screen_shot_2012-01-22_at_11.34.46_AM.png]]
 * This equation can also be written as sinØ crit = n 2 /n 1.

Lesson 4
How is light dispersed by Prisms?
 * The separation of visible light into its colors is known as dispersion. We know that each color is characteristic of having distinct wavelengths as well as distinct frequencies from one another. Because of this, the change in wavelength causes a change in the angle of refraction when light goes through a prism. Because of this change in refraction angle between colors, the colors are dispersed slightly, so slightly that they appear to still be touching.
 * [[image:u12l2a3.gif]]
 * 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. Because of the different indices of refraction for the different wavelengths of visible light, the angle of deviation varies with wavelength.
 * [[image:u14l4a1.gif]]

How are rainbows formed?
 * Rainbows are formed by the dispersion of light in lots of water droplets that are in the sky and the clouds. Like with the prism, the water droplets disperse the colors based upon their wavelength. The angle of deviation causes the colors to vary in location in order of their wavelengths, which is why the rainbow is in the order of ROYGBIV.
 * [[image:u14l4b1.gif]]
 * The reason that we see the color deviation is based upon the angle that we look at the rainbow. Every color is refracted by each raindrop, but only the colors refracted directly at the viewer will be seen from that water droplet.
 * [[image:u14l4b3.gif]]

What causes Mirages?
 * A mirage is a phenomenon that creates the illusion of water and results from the refraction of light through a non-uniform medium. Mirages are most commonly observed on sunny days when driving down a roadway. The role of the sun is to heat the roadway to high temperatures. This heated roadway in turn heats the surrounding air, keeping the air just above the roadway at higher temperatures than that day's average air temperature. Hot air tends to be less optically dense than cooler air. As such, a non-uniform medium has been created by the heating of the roadway and the air just above it. This change in air density causes a change in lights velocity through the air and therefor a bend in path. This bend is perceived as the result of reflection by the brain, and therefor thinks that it is caused by a puddle of water. When you reach the location of the image, however, there is no puddle, and it appears to have moved farther up the road.
 * [[image:u14l4c2.gif]]

Lesson 5
What is the anatomy of a Lens?
 * A lens is a carefully ground or molded piece of transparent material that refracts light rays in such as way as to form an image. Lenses can be thought of as a series of tiny refracting prisms, each of which refracts light to produce their own image. When these prisms act together, they produce a bright image focused at a point. There are two types of lenses, a converging lens and a diverging lens. A converging lens converges the rays that pass through it towards the principal axis. The diverging lens scatters light that passes through it away from the principal axis.
 * Two main types of lenses are a double convex lens and a double concave lens. The double convex lens is converging on both sides and has the properties of a converging lens. The double concave lens is diverging on both sides and has the properties of a diverging lens.
 * It is important to know that for diagrams, the principal axis runs perpendicular to the lens, and the vertical axis runs in the middle of the lens on the wider ends of the lens. On the principal axis are the vertex, the focal point, and the value 2F, which is twice the distance from the lens as the focal point.
 * [[image:u14l5a1.gif]]

What is refraction by lenses?
 * A lens is shaped to create clear images, and they refract the light as it passes through. The light is refracted as it enters the lens as well as when it exits the lens, changing the direction of the light ray. We know that the double convex lens will refract the light towards the principal axis, and if a series of light rays hit the lens parallel to the principal axis they would all intercept at the focal point, and an image would be created. For a double concave lens we know that it diverges light rays, so an image will not be created on the other side of the lens. We can, however, extend the line of the refracted ray to the same side of the lens as where the person is looking from and see that they all intersect at that focal point. This point is where the image appears.
 * Refraction rules for a converging lens
 * 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.
 * 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.
 * 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.
 * Refraction rules for a diverging lens
 * 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).
 * 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.
 * 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.

How are images formed?
 * Suppose that a light bulb is placed in front of a concave mirror; the light bulb will emit light in a variety of directions, some of which will strike the mirror. Each individual ray of light will reflect according to the law of reflection. Upon reflecting, the light will converge at a point. At the point where the light from the object converges, a replica or likeness of the actual object is created; this replica is known as the image. Concave mirrors make real images.
 * [[image:u13l3b2.gif]]
 * Converging lenses can produce both real and virtual images while diverging images can only produce virtual images. The process by which images are formed for lenses is the same as the process by which images are formed for plane and curved mirrors. Images are formed at locations where any observer is sighting as they view the image of the object through the lens. In the case of a diverging lens, the image location is located on the object's side of the lens where the refracted rays would intersect if extended backwards. Every observer would be sighting along a line in the direction of this image location in order to see the image of the object.
 * [[image:u14l5c1.gif]][[image:u14l5c2.gif]]

Converging Lenses-Ray Diagrams
 * Double Convex Lens:
 * 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.
 * 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.
 * An incident ray that passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens.
 * [[image:u14l5da5.gif]]

Converging Lenses-Object Image Relations
 * Case 1: the object is located //beyond// the 2F point--> The image is inverted and located between F and 2F on other side and is reduced.
 * Case 2: the object is located at the 2F point--> The image is inverted, located at 2F, and is the same size.
 * Case 3: the object is located between the 2F point and the focal point (F)--> The image is beyond 2F, inverted, and enlarged.
 * Case 4: the object is located at the focal point (F)--> NO IMAGE
 * Case 5: the object is located //in front of// the focal point (F)--> The image is between F and 2F of the same side as object, is right-side up, and enlarged.
 * [[image:u14l5db7.gif]]

Diverging Lenses-Ray Diagrams
 * 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).
 * 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.
 * 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.
 * [[image:u14l5ea7.gif]]

Diverging Lenses-Object Image Relations
 * in each case, the image is
 * located on the object' side of the lens
 * a virtual image
 * an upright image
 * reduced in size (i.e., smaller than the object)
 * [[image:u14l5eb3.gif]]

The mathematics of Lenses
 * Two major equations are used for calculations with the object, image, and focal point.
 * [[image:u13l3f1.gif]] uses the distance of the object and the focal length to find the distance of the image.
 * [[image:u13l3f2.gif]]uses the heights or distances to find the magnification of the lens, or can be used with the distances and height of the object to find the height of the image.

Lesson 6
What is the anatomy of the eye?
 * cornea- transparent opening in the front of the eye
 * pupil- opening in eye behind the cornea
 * iris- the colored part of the eye, it is a diaphragm capable of stretching or reducing the size of the opening to limit the amount of light that enters the eye.
 * crystalline lens- layers of a fibrous material with an index of refraction of 1.4. It can change its shape to make images clearer.
 * ciliary muscles- muscles that change the shape of the lens to produce an image at the back of the eyeball.
 * retina- inner surface of the eye. It has rods and cones to detect intensity and frequency of incoming light.
 * optical nerve- a network of nerve cells bundled together in the back of the eyeball.
 * [[image:u14l6a1.gif]]

What is the image formation and detection? >
 * 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 image will be inverted, reduced in size, and real. Quite conveniently, the cornea-lens system produces an image of an object on the retinal surface.

The wonder of accomodation
 * The ability of the eye to adjust its focal length is known as accommodation. Since a nearby object (small dobject) is typically focused at a further distance (large dimage), the eye accommodates by assuming a lens shape that has a shorter focal length. So for nearby objects, the ciliary muscles contract and squeeze the lens into a more convex shape. This increase in the curvature of the lens corresponds to a shorter focal length. On the other hand, a distant object (large dobject) is typically focused at a closer distance (small dimage).

What is farsightedness and how do you correct it?
 * farsightedness is the inability of the eye to focus on nearby objects. The farsighted eye has no difficulty viewing distant objects. But the ability to view nearby objects requires a different lens shape - a shape that the farsighted eye is unable to assume. As a result, the image created by the lens of the eye is in a position that is behind the retina and cannot be seen clearly. To fix this problem, a converging lens must be placed in front of the eyes to refract the light so that the image is on the retina.
 * [[image:u14l6d2.gif]]

What is nearsightedness and how do you correct it?
 * Like farsightedness, the problem is that the eye cannot make the lens into the appropriate shape for the image to appear on the retina. This problem can be fixed by placing a diverging lens in front of the eye, refracting the light before it reaches the eyes.
 * [[image:u14l6e2.gif]]