Ch24-26_RabinR

= Chapter 24-27: Optics and Light = toc

Chapter 24: Guiding Questions
1. Identify the contributions from each of the following scientists to the study and the nature of light. a) Newton - Investigated the refraction of light and discovered that a prism could break white light into a spectrum of colors b) Huygens - Achieved note for his argument that lights consists of waves c) Grimaldo - The first to make accurate observations on the diffraction of light, and coined the word 'diffraction' d) Young - Studied the interference of light waves demonstrating his theory through multiple experiments e) Maxwell - Demonstrated that electricity, magnetism and light were all from the same phenomenon, the electromagnetic field, developing the Maxwell Equations f) Hertz - Discovered that light was a form of electromagnetic radiation, units of waves were named after him g) Einstein - Created the quantum theory of light 2. Measuring the speed of light was challenging. Describe the results of the experiments by each of the following scientists.  a) Galileo - Although he was unable to calculate an exact velocity, he proved that light traveled faster than sound b) Roemer - Made the first quantitative measurements of the speed of light c) Fizeau - Found that light traveled at 3.13 x 1 08 m/s, which was 5% higher than the true theoretical value 3. What are the 2 biggest differences between an electromagnetic wave and a mechanical wave? While an electromagnetic wave requires no medium, mechanical waves do. In addition, electromagnetic waves are 3-dimensional while mechanical waves are 2-dimensional. 4. Describe the EM spectrum. 5. Describe Maxwell's experiment. 6. Apply the Doppler Affect to light. Using the Doppler Affect equation, one can find the change in frequency of light as the source/observer move to and from each other. 7. What is polarization? The process in which light undergoes to restrict vibrations completely or in one direction. 8. Describe Malus' Law. Used to find the intensity of light after having gone through polarization. 9. Contrast the polarizer and the analyzer. Light may be polarized several times. The polarizer is the first filter light goes through while the analyzer is the second filter light goes through. 10. When does polarization occur in nature? As light travels through the atmosphere, scattering occurs which creates blue skies and yellow light. 11. Two polarizing filters are placed in the path of a beam of light with an intensity measured to be 820 W/m^2. The analyzer is then rotated until the intensity is at a maximum. Assuming that the two filters are perfect: a) What is the relative orientation of the transmission axes of the filters when maximum intensity is transmitted? 0 degrees  b) What should the intensity of the light beam be in this orientation? S= So(costheta)^2 S=820/2 S= 410 W/m^2 c) What is the relative orientation of the transmission axes of the filters when minimum intensity is transmtted? 90 degrees  d) What will be the intensity of the light transmitted by the filters when the intensity is at a minimum 0 W/m^2 e) If a third polarizer is inserted between the first two polarizers (as oriented in c) and the angle of this third polarizer is rotated until the angle between it and the first polarizer is 25 degrees. What will be the intensity transmitted by all three? S=So(costheta)^2 S= 510 cos^2(25) S= 337 W/m^2 S= 337cos^2(65) S= 60 W/m^2

Chapter 25: Guiding Questions
1. Distinguish between wave fronts and rays. Wave fronts are surfaces that all emit light through the same medium while rays are single beams of light. 2. Distinguish between specular and diffuse reflection. 3. What is the law of reflection? States that a normal line divides the angle between the incident and reflected ray into two equal angles. 4. Draw a diagram identify rays and angles. 5. A ray of light in air is incident on an air-to-glass boundary at an angle of 30 degrees with the normal. If the index of refraction of glass is 1.65, what is the angle of the ray reflected off the glass surface with respect to the normal? 30 degrees 6. List the 4 ways we describe images. In other words what are the characteristics of images? Type: Real or virtual Location: Relative to lens/mirror and focal point Orientation: Upright or inverted Size: Unchanged, reduced, enlarged 7. Distinguish between real and virtual images. Real images are those that are created where light actually exists. Real images are always inverted. Virtual images are those that are created at points where light does not actually pass through. Virtual images are always upright. 8. What is magnification? Magnification is the increase or decreases of the image in comparison to its original object. Magnification is defined by the following equation. 9. What are the image characteristics of an object viewed in a plane mirror? Type: Virtual Location: Behind the mirror Orientation: Upright Size: Unchanged 10. What is the reference position for all distances measurements on mirror or lens problems? The vertex which is defined by the location of the mirror or the lens. 11. What is the sign convention for images in mirrors or lenses? 12. Distinguish between concave and convex mirrors. Concave mirrors focus light on a specific point and are converging while convex mirrors spread light out and are diverging. 13. Identify the following terms: a) Principal Axis - Imaginary line that goes through the center of the mirror b) Focal Point - Midway between the mirror and center of curvature c) Focal Length - Distance between the focal point and the mirror d) Center of Curvature - center of mirror from which the mirror was cut e) Radius of Curvature - distance between the center of curvature and the mirror 15. What are the image characteristics of an object viewed in a concave mirror? 16. What are the image characteristics of an object viewed in a convex mirror? Type: Virtual Location: Behind the mirror Orientation: Upright Size: Reduced 17. What image will be produced when the object viewed is located at the focal point of the mirror? There will be no image for a concave mirror however the image characteristics for a convex mirror will remain constant when the object is located at the focal point of the mirror. 18. What are several applications of mirrors (besides looking at your own gorgeous features)? Mirrors are often used when backing out of a driveway on busy streets. It helps the driver see oncoming traffic and avoid accidents. It is also used by doctors more specifically dentists to see areas of the body that are not normally visible.

Pre-Lab: Polarization
1. The objective is stated in the title. What is your hypothesis? (Attempt to answer the the question, to the best of your knowledge.) The intensity of light will have a direction relationship with the cosine squared of the angle. 2. What is the rationale for your hypothesis? (Provide detailed reasoning here. This may take the form of a light of what you already know bout he topics, with a summary at the end.) My hypothesis is based off of Malus' Law which can be defined as. 3. How do you think you might test this hypothesis? (What might you measure and who?) By shooting a beam of light through polarizers at multiple angles, we should be able to test the intensity and compare it to the theoretical intensity. 4. Read the procedure and calculations. make any tables in order to organize your data and calculations. 3. Light is shown through a set of 2 polarizing filters. When is transmitted light at maximum intensity? Minimum intensity? Light is transmitted at maximum intensity when the angle between the 2 filters is 0 degrees and light is transmitted at minimum intensity when the angle between the 2 filters is 90 degrees. 4. What is the relationship of the intensity of transmitted light to the angle of the polarizers between 0 and 90 degrees? The intensity of transmitted light is inversely proportional to the angle between the polarizers between 0 and 90 degrees.

Lesson 1D
What is polarization? A light wave that is vibrating in more than one plane is referred to as **unpolarized light**. In general, it is helpful to picture unpolarized light as a wave that has an average of half its vibrations in a horizontal plane and half of its vibrations in a vertical plane. It is possible to transform unpolarized light into **polarized 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**.
 * Method 4: SQ3R**

What is polarization by Use of a Polaroid Filter? Polaroid filters are made of a special material that is capable of blocking one of the two planes of vibration of an electromagnetic wave. In this sense, a Polaroid serves as a device that filters out one-half of the vibrations upon transmission of the light through the filter. 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.

What is polarization by reflection? By refraction? By scattering? 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. Polarization can also occur by the refraction of light. 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. 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. This newly generated wave strikes neighboring atoms, forcing their electrons into vibrations at the same original frequency. These vibrating electrons produce another electromagnetic wave that is once more radiated outward in all directions. This absorption and reemission of light waves causes the light to be scattered about the medium.

Lesson 2A
What is the electromagnetic and visible spectra? Electromagnetic waves are produced by a vibrating electric charge and as such, they consist of both an electric and a magnetic component. Electromagnetic waves exist with an enormous range of frequencies. This continuous range of frequencies is known as the **electromagnetic spectrum**. The longer wavelength, lower frequency regions are located on the far left of the spectrum and the shorter wavelength, higher frequency regions are on the far right. The visible light region is the very narrow band of wavelengths located to the right of the infrared region and to the left of the ultraviolet region. Since this narrow band of wavelengths is the means by which humans see, we refer to it as the **visible light spectrum**. Each individual wavelength within the spectrum of visible light wavelengths is representative of a particular color. The separation of visible light into its different colors is known as **dispersion**. Each color is characteristic of a distinct wavelength; and different wavelengths of light waves will bend varying amounts upon passage through a prism. For these reasons, visible light is dispersed upon passage through a prism. Dispersion of visible light produces the colors red (R), orange (O), yellow (Y), green (G), blue (B), and violet (V).
 * Method 4: SQ3R**

Lesson 1A-D
What is the role of light to sight? The bottom line is: without light, there would be no sight. The visual ability of humans and other animals is the result of the complex interaction of light, eyes and brain. We are able to see because light from an object can move through space and reach our eyes. Once light reaches our eyes, signals are sent to our brain, and our brain deciphers the information in order to detect the appearance, location and movement of the objects we are sighting at. The objects that we see can be placed into one of two categories: luminous objects and illuminated objects. **Luminous objects** are objects that generate their own light. **Illuminated objects** are objects that are capable of reflecting light to our eyes. What is the line of sight? This directing of our sight in a specific direction is sometimes referred to as the **line of sight**. The principle states: 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. As you sight at the image of an object in the mirror (whether it be a stoppered pencil or any object), light travels along your line of sight towards your eye. The object is being illuminated by light in the room; a countless number of rays of light are reflecting off the object in a variety of directions. When viewing the image of the object in a plane mirror, one of these rays of light originates at the object location and first travels along a line towards the mirror (as represented by the blue ray in the diagram below). This ray of light is known as the **incident ray** - the light ray approaching the mirror. The incident ray intersects the mirror at the same location where your line of sight intersects the mirror. The light ray then reflects off the mirror and travels to your eye (as represented by the red ray in the diagram below); this ray of light is known as the **reflected ray**. What is the law of reflection? If a ray of light could be observed approaching and reflecting off of a flat mirror, then the behavior of the light as it reflects would follow a predictable //law// known as the **law of reflection**. The diagram below illustrates the law of reflection.
 * Method 4: SQ3R**

**Incident ray** (labeled **I** in the diagram) - ray of light approaching the mirror **Reflected ray** (labeled **R** in the diagram) - ray of light that leaves the mirror **Angle of incidence** - The angle between the incident ray and the normal **Angle of reflection** - angle between the reflected ray and the normal 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. What is specular reflection? Diffuse reflection? Reflection off of smooth surfaces such as mirrors or a calm body of water leads to a type of reflection known as **specular reflection**. Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to a type of reflection known as **diffuse reflection**.
 * N ** **ormal line** (labeled **N** in the diagram) - At the point of incidence where the ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror. The normal line divides the angle between the incident ray and the reflected ray into two equal angles.

Lesson 2A-F
Why is an Image Formed? The image location is located at that position where observers are sighting when viewing the image of an object. When each line of sight is extended backwards, each line will intersect at the same point. This point is the image point of the object. __Image Location__- the one location in space where it seems to every observer that the light is diverging from - the image location is directly across the mirror from the object location and an equal distance from the mirror //An image is formed because light emanates 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.// What are the image characteristics for plane mirrors? **Image location** - the location in space where all the reflected light appears to diverge from **Virtual image** - 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** - formed by curved mirrors. Such images are formed on the same side of the mirror as the object and light passes through the actual image location. **Magnification** - The ratio of the image dimensions to the object dimensions
 * Method 4: SQ3R**

In conclusion, plane mirrors produce images with a number of distinguishable characteristics. 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 are the ray diagrams for plane mirrors? **Ray diagram** - 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 reflected ray.

Step 1 Use the principal that object distance is equal to image distance. Pick one extreme of the object and measure its distance from the mirror. Mark off the same distance on the other side. Repeat this for all extremes of the object until the complete location and size is determined.

Step 2 Use the line of sight principal. Draw a bold line for the reflected ray, and a dashed line for the extension of this reflected ray. The arrowhead should point towards the eye.

Step 3 Draw the incidence ray from the extreme of the object to the point of incidence on the mirrors surface. Arrowhead should point towards the mirror.

Step 4 Repeat steps 2 + 3 for all other extremities of the object.

What portion of a mirror is required to view an image? To see the image of his feet, he must sight along a line towards his feet; and to see the image of the top of his head, he must sight along a line towards the top of his head. 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 order to view his image, the man must look as low as point Y (to see his feet) and as high as point X (to see 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.

Lesson 3A-G
What is the anatomy of a curved mirror? Spherical mirrors are curved mirrors with a spherical shape, portion of a sphere that was sliced away and silvered on one side to form a reflecting surface. There are two kinds of curved mirrors, concave and convex. Concave mirrors were silvered on the inside of the sphere while convex mirrors were silvered on the outside of the sphere. The anatomy of a curved mirror: C - center of curvature: point in the center of the sphere from which the mirror was sliced A - vertex: point on the mirror's surface where the principle axis meets the mirror F - focal point: midway between the vertex and the center of curvature R - radius of curvature: distance from the vertex to the center of curvature f - focal length: distance from the mirror to the focal point
 * Method 4: SQ3R**

What is the reflection of light and image formation? The angle of incidence equals the angle of the reflected ray Concave mirrors produce real images, it still appears to an observer as though light is diverging from the real image only in addition light is actually passing through the image location as well.

What are the laws of reflection regarding concave mirrors? Two rules of reflection for concave mirrors: -Any incident ray traveling parallel to the principal axis on th 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

What are ray diagrams for concave mirrors? Step 1: Pick a point on the top of the object and draw two incident rays traveling towards the mirror. Using a straight edge, accurately draw one ray so that it passes exactly through the focal point on the way to the mirror. Draw the second ray such that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel. Step 2: Once these incident rays strike the mirror, reflect them according to the two rules of reflections or concave mirrors.

The ray that passes through the focal point on the way to the mirror will reflect and travel parallel to the principal axis. Use a straight edge to accurately draw its path. The ray that traveled parallel to the principal axis on the way to the mirror will reflect and travel through the focal point. Place arrowheads upon the rays to indicate their direction of travel. Extend the rays past their point of intersection. Step 3: Mark the image of the top of the object.

The image point of the top of the object is the point where the two reflected rays intersect. If your were to draw a third pair of incident and reflected rays, then the third reflected ray would also pass through this point. This is merely the point where all light from the top of the object would intersect upon reflecting off the mirror. Of course, the rest of the object has an image as well and it can be found by applying the same three steps to another chosen point.

Step 4: Repeat the process for the bottom of the object.

The goal of a ray diagram is to determine the location, size, orientation, and type of image that is formed by the concave mirror. Typically, this requires determining where the image of the upper and lower extreme of the object is located and then tracing the entire image. After completing the first three steps, only the image location of the top extreme of the object has been found. Thus, the process must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object. At this point the entire image can be filled in.



What are image characteristics for concave mirrors? Case 1: the object is located beyond the center of curvature so the image will be located somewhere in between the C and the F, image is inverted, and reduced in size, real image. Case 2: the object is located at the center of the curvature so the image will also be located at the C, image is inverted, and size is unchanged, real image Case 3: the object is located between the C and F, image will be beyond the C, inverted, larger in size, real image Case 4: the object is located at the focal point so NO IMAGE FOUND! Case 5: the object is located in front of the F, located somewhere on the opposite side of the mirror, upright image, magnified (greater dimensions), virtual image

What is the mirror equation for concave mirrors? The mirror equation and magnification equation will express quantitatively the characteristics of the image. Mirror Equation Magnification

What is spherical aberration? An aberration is a departure from the expected or proper course. This defect prohibits the mirror from focusing all the incident light from the same location on an object to a precise point. Rays that strike the outer edges of the mirror fail to focus in the same precise location as light rays that strike the inner portions of the mirror.The two incident rays that strike the outer edges (top and bottom) of the concave mirror fail to pass through the focal point. This is a //departure from the expected or proper course//.

Lesson 4A-D
1. How are images formed in convex mirrors?
 * Method 4: SQ3R**



Convex mirrors form virtual images, located behind the mirror.

__Virtual Image-__ Light d oes not actually pass through the image location. It only appears to observers as though all the reflected light from each part of the object is diverging from this virtual image location.

__Image Location-__ point of intersection of all extended reflected rays

__Two rules of reflection for convex mirrors:__

2. How do you draw ray diagrams for convex mirrors? Step 1: draw one ray so that it goes towards the focal point on the opposite side of the mirror to the point of incidence. Draw the second ray parallel to the principal axis.
 * 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] __.



Step 2: When the rays strike the mirror, reflect them based on the two rules of reflection for convex mirrors



Step 3: Locate and mark the image. The image occurs where the two rays of reflection intersect.



Step 4: Repeat 3 for the bottom of the object If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object.

3. What are the image characteristics for convex mirrors? IMAGES FROM CONVEX MIRRORS ARE ALWAYS 4. What are the mirror/magnification equations for convex mirrors? Mirror Equation Magnification Equation
 * located behind the convex mirror
 * a virtual image
 * an upright image
 * reduced in size (i.e., smaller than the object)

Lesson 1A-D
After reading the material, answer the following questions: 1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. From class, I understood really well how to find the index of refraction. It was extremely clear that using the equation will get me the correct value. I also understood the differences when traveling from fast to slow medium and vice versa. 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. On the other hand, 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. 2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding. I wasn't really sure exactly how refraction was applied to sight. It was not very clear to me how it would be depicted. The lab based on refraction really cleared this up for me and I now understand exactly when should be seen. 3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question. Why is refraction caused? 4. What (specifically) did you read that was not gone over during class today? We did not go over optical density which is related 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
 * Method 2a: Directed Reading (as a Follow-Up)**

Lesson 2A-D
What is the angle of refraction? Refraction - the bending of the path of a light wave as it passes across the boundary separating two media, caused by the change in speed experienced by a wave when it changes medium Incident Ray - that shows the direction that light travels as it approaches the boundary Refracted Ray - shows the direction that light travels after it has crossed over the boundary
 * Method 4**

What is Snell's law? This study of the refraction of light as it crosses from one material into a second material yields a general relationship between the sines of the angle of incidence and the angle of refraction. This general relationship is expressed by the following equation: . This relationship between the angles of incidence and refraction and the indices of refraction of the two media is known as **Snell's Law**. Snell's law applies to the refraction of light in any situation, regardless of what the two media are.

Lesson 3A-C
What is total internal reflection? **Total internal reflection** - the reflection of the total amount of incident light at the boundary between two media
 * Method 4**

Total internal reflection (TIR) is the phenomenon that 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 more dense medium and approaching the less dense medium.
 * the angle of incidence is greater than the so-called critical angle.

What is the critical angle? Critical angle - the angle of incidence that provides an angle of refraction of 90-degrees

Lesson 4A-C
How is light dispersed by a prism? **dispersion** - separation of visible light into its different colors is known These colors are often observed as light passes through a triangular prism. Upon passage through the prism, the white light is separated into its component colors - red, orange, yellow, green, blue and violet. What is the angle of deviation? **angle of deviation** - the amount of overall refraction caused by the passage of a light ray through a prism 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. How is a rainbow formed? In a formation of a rainbow, light changes mediums from air to water when it goes through a droplet. Then the light bends towards the normal, light refracts into the droplet, internally reflects, and then refracts out of the droplet, and a collection of suspended droplets in the atmosphere that are capable concentrating the dispersed light at angles of deviation of 40-42 degrees relative to the original path of light from the sun What is a mirage? **mirage** - an optical 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.
 * Method 4**

Lesson 5A-F
What is the anatomy of a lens? **lens** - carefully ground or molded piece of transparent material that refracts light rays in such as way as to form an image **Converging lens** - a lens that converges rays of light that are traveling parallel to its principal axis. Converging lenses can be identified by their shape; they are relatively thick across their middle and thin at their upper and lower edges. **Diverging lens** - a lens that diverges rays of light that are traveling parallel to its principal axis. Diverging lenses can also be identified by their shape; they are relatively thin across their middle and thick at their upper and lower edges.
 * Method 4**

**Principal axis** - imaginary line passing through the center of the sphere and attaching to the mirror in the exact center of the lens **Vertical axis** - imaginary line that bisects the symmetrical lens into halves **Focal point** - light rays incident towards either face of the lens and traveling parallel to the principle axis will either converge or diverge, if the light rays converge, then they will converge to a point, this point is known as the focal point **Focal length** - distance from the mirror to the focal point **2F point** - point on the principle axis that is twice as far from the vertical axis as the focal point

What are the rules of refraction for a converging lens? Diverging lens? 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.



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.



What are the ray diagrams and image characteristics for a converging lens?

five incident rays are drawn along with their corresponding refracted rays. Each ray intersects at the image location and then travels to the eye of an observer. Every observer would observe the same image location and every light ray would follow the Snell's Law of refraction. Yet only two of these rays would be needed to determine the image location since it only requires two rays to find the intersection point. Of the five incident rays drawn, three of them correspond to the incident rays described by our [|three //rules// of refraction] for converging lenses. We will use these three rays through the remainder of this lesson, merely because they are the easiest rays to draw. Certainly two rays would be all that is necessary; yet the third ray will provide a check of the accuracy of our process

Image characteristics: - Real -Real - Inverted -Inverted - Same Size -Larger

In Front of Focal Point:

- Virtual - Upright - Larger

At Focal Point: No image

What are the ray diagrams and image characteristics for a diverging lens?
 * located on the object' side of the lens
 * a virtual image
 * an upright image
 * reduced in size (i.e., smaller than the object)

What are the mathematics behind lenses? The lens equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). The equation is stated as follows: 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). The magnification equation is stated as follow: These two equations can be combined to yield information about the image distance and image height if the object distance, object height, and focal length are known.

What is the sign convention for lenses? The sign conventions for the given quantities in the lens equation and magnification equations are as follows:
 * f is + if the lens is a double convex lens (converging lens)
 * f is - if the lens is a double concave lens (diverging lens)
 * di is + if the image is a real image and located on the opposite side of the lens.
 * di is - if the image is a virtual image and located on the object's side of the lens.
 * 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)

Lesson 6A-E
What is the anatomy of an eye?
 * Method 4**

**Cornea** - In the front of the eyeball is a transparent opening, thin membrane that has an index of refraction of approximately 1.38, has the dual purpose of protecting the eye and refracting light as it enters the eye. **Pupil** - after light passes through the cornea, a portion ofit passes through an opening known **Iris** - like the aperture of a camera, the size of the pupil opening can be adjusted by the dilation of the **iris**, the iris is the colored part of the eye - being blue for some people and brown for others (and so forth); it is a diaphragm that is capable of stretching and reducing the size of the opening **Crystalline lens** - light that passes through the pupil opening, will enter the crystalline lens. The crystalline lens is made of layers of a fibrous material that has an index of refraction of roughly 1.40. Unlike the lens on a camera, the lens of the eye is able to change its shape and thus serves to fine-tune the vision process. **Ciliary muscles** - the lens is attached to the ciliary muscles. These muscles relax and contract in order to change the shape of the lens. By carefully adjusting the lenses shape, the ciliary muscles assist the eye in the critical task of producing an image on the back of the eyeball. **Retina** - inner surface of the eye. **Optic nerve** - network of nerve cells is bundled together in the very back of eyeball

How does the eye detect and form images?

4. How is farsightedness corrected? Farsightedness/Hyperopia- the inability of the eye to focus on nearby objects, must assist the lens in in refracting the light, the lens can no longer assume the convex and highly curved shape that is, required to view nearby objects, converging lens will refract light before it enters the eye and decrease the image distance

5. How is nearsightedness corrected? Nearsightedness/Myopia- inability to focus on distant objects, equip the eye with a diverging lens, the light is focused in front of the retina, so a diverging lens will serve to diverge light before it reaches the eye, light will then be converged by the cornea and lens to produce an image on the retina