Optics

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toc = = = = = = =CH 24=

**Polarization PreLab**

 * 1) What is your hypothesis?
 * 2) There is a direct relationship between the intensity of the cosine squared of the angle. The rationale for this is the equation: [[image:samfihmaap/Screen_shot_2011-12-21_at_9.32.03_AM.png caption="Screen_shot_2011-12-21_at_9.32.03_AM.png"]]. We will test this hypothesis by varying the transmittance of light using a setup with polarizers, a light sensor, and light sources.
 * 3) Read the entire labsheet through. Make a table.


 * Percent Transmittance || Angle between Polarizers || Inensity ||


 * 1) Light is shown through a set of two polarizing filters. When is transmitted light at maximum intensity? Minimum intensity?
 * 2) Intensity is at a maximum when the two polarizing filters are parallel (0 degrees).
 * 3) Intensity is at a minimum when the two polarizing filters are perpendicular (90 degrees).
 * 4) What is the relationship of the intensity of transmitted light to the angle of the polarizers between 0 and 90 degrees?
 * 5) The intensity of transmitted light is inversely proportional to the angle of the polarizers between 0 and 90 degrees.

Lesson 1D - Polarization
A polaroid filter is made out of special material that blocks out one of the two planes that light vibrates in. As a result, this filter effectively cuts the intensity of light passing through it in half. The filter is made of long-chain molecules that are all aligned in the same direction, and light molecules that vibrate in parallel to this direction are allowed to pass through and the rest are blocked. The alignment of these molecules gives the filter a polarization axis.
 * How to Polarize by use of a Polaroid Filter**






 * How to polarize by reflection?**

Unpolarized light can undergo polarization by being reflected off nonmetal surfaces. The amount of polarization is dependent on the angle that the light approaches and the material that the surface is made of.




 * How to polarize by refraction?**

Light can also be polarized by refraction and this refraction occurs when light passes from one material to another. At the surface of the materials the beam changes direction and this causes polarization**.**




 * How to polarize by scattering?**

Polarization can also occur when light is scattered while traveling through a medium. When light strikes the atoms of a material the electrons vibrate and create electromagnetic waves. These atoms cause neighboring electrons in atoms to start vibrating as well. This absorption and reemission causes light to scatter throughout the medium. This scattered light is partially polarized.


 * What are applications of polarization?**

Polarization is used in glare-reducing sunglasses and in the production of 3D movies and polaroid filters are used in stress analysis tests on transparent plastics.

**Lesson 2A**
The electromagnetic spectrum is the continuous range of frequencies of electromagnetic waves. The lower the frequency means the longer the wavelength of the wave and the higher the frequency means the shorter the wavelength of the wave.
 * What is the electromagnetic spectrum?**




 * What is the visible light spectrum?**

The region in between the infrared and ultraviolet sections is referred to as the visible light spectrum and it is a very small part of the entire electromagnetic spectrum. It is the only part of the spectrum that humans can see with the naked eye. The wavelengths of the visible light section range from 700nm to 400nm. Each wavelength in the spectrum signifies a color. Separation of light into different colors is referred to as dispersion.

=**CH 25**=

**Guiding Questions**




**Lesson 1 (a-d)**

 * What is the role of light to sight?**

Light is very important to sight because light enables sight. We are able to see because light from an object can move through space and reach our eyes. Once the light reaches our eyes, our brain receives these signals, decodes them, and we see the image that we are looking at. There are two different types of objects, luminous and illuminated. Luminous objects produce their own light and illuminated objects reflect light to our eyes. The sun is a luminous object and humans are illuminated objects.


 * What is line of sight?**

The directing of sight in a certain direction is referred to as line of sight. To see an object, one must view along a line at that object and light from that object will travel to your eyes along that line. Our eyes only see a portion of the light that is reflected off objects as the rays diverge. There are two types of rays: incident ray and reflected ray. The incident ray is the ray that comes off the object and travels toward the mirror. The reflected ray is the ray that reflects off the mirror and travels toward your eyes. For plane mirrors, the object distance is the same as the image distance (distance from mirror to image).


 * What is the law of reflection?**

The law of reflections states that the angle of incidence the incident ray makes with the normal to the mirror will be equal to the angle of reflection the reflected ray makes with the normal to the mirror.




 * What is the difference between specular and diffuse reflection?**

Reflection off smooth surfaces such as water is referred to as specular reflection. Reflection of rough surfaces such as paper is referred to as diffuse reflection.




 * Why does a rough surface diffuse a light beam?**

The law of reflection has to be observed for every ray so each ray will hit the surface with a different angle of incidence resulting in different angles of refraction for each light beam, which results in the light being diffused.

**Lesson 2**
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. The image location is where observers are sighting when viewing the image of an object. It is the location behind the mirror where all the light appears to diverge from.
 * Why is an image formed?**




 * What are image characteristics of a plane mirror?**

The image characteristics of a plane mirror are as follows: virtual, upright, same size as object, and behind the mirror at the same distance as the object is to the mirror, left-right reversal.


 * What is a ray diagram?**

A ray diagram is a diagram that traces the path of light from the object to the mirror and from the mirror to the eye. Rays are drawn for the incident and reflected ray.


 * What portion of the mirror is required to view an image**?

Exactly one half the height of the object is required for the mirror in order view the entire image of the object.




 * What are right angle mirrors?**

A right angle mirror produces three images. A right angle mirror consists of two separate mirrors that are joined at right angles.




 * What are other multiple mirror systems?**

There are several other multiple mirror systems. The diagram below shows these systems and how many images are formed in these systems.



**Lesson 3**

 * What is the anatomy of a curved mirror?**

Curved mirrors come in two different varieties: concave and convex. Concave mirrors can be considered as a part of the inside of a sphere. The line going through the center of the sphere of which the mirror was taken from referred to as the principal axis; this axis runs through the center of the mirror as well. The center of the sphere is referred to as the center of curvature and the distance from this point to the mirror is referred to as the radius of curvature. Half this distance is the focal point of the mirror.




 * How is an image formed in a concave mirror?**

All mirrors follow the law of reflection regardless of curvature and a concave mirror is no exception. Upon reflecting the light will converge at a point and this is where the image will be located. The image is a replica of the object. Concave mirrors can form real or virtual images.




 * What are the two rules of reflection for concave mirrors?**

The two rules are as follows:

- 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.

The following pictures illustrate these rules. The blue ray is the incident ray and the red ray is the reflected ray.




 * What is the ray diagram for concave mirrors and how to draw it?**

How to draw it:

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. The image point of the top of the object is the point where the two reflected rays intersect. 4. Repeat the process for the bottom of the object.

Here is what it should look like:




 * What are the image characteristics for concave mirrors?**

The characteristics are as follows:

Case 1: the object is located //beyond//the center of curvature (C) -- center of curve, inverted, reduced, real image Case 2: the object is located at the center of curvature (C) -- center of curve, inverted, normal size, real image Case 3: the object is located between the center of curvature (C) and the focal point (F) -- beyond center of curve, inverted, magnified, real image 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) -- opposite side of the mirror, upright, magnified, virtual image




 * What are the mirror equations?**



f = focal distance do = object distance di = image distance



M = Magnification of the image. M > 1 means the image is enlarged. M < 1 means the image is reduced. M = 1 means image is same size as object. A negative M means the image is inverted. hi = image height ho = object height di = image distance do = object distance


 * What is spherical aberration?**

Inherent in any mirror that is in the shape of a sphere is an aberration called spherical aberration. This aberration or defect of spherical mirrors prevents the mirror to focus all the light to a single point. The light rays that strike the outer most portions of the mirror are affected the most and they are said to depart from the proper or expected course. The spherical aberration of curved mirrors results in a blurry image. Parabolic mirrors eliminate any sort of aberration.



**Lesson 4**

 * How are images formed in convex mirrors?**

A convex mirror is referred to as a diverging mirror as reflected light rays diverge and do not meet at any single point. Convex mirrors are shaped opposite to that of concave mirrors; convex mirrors are taken from the outside of a sphere. The center of curvature and focal point is located on the opposite side of the object opposite that of the concave mirror.



Because light never converges at a point in a convex mirror, the image is said to be virtual.



The two rules of reflection for convex mirrors are as follows:

- 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.


 * What is the ray diagram for convex mirrors and how is it drawn?**

To draw the ray diagram, follow the above rules of reflection.




 * What are the image characteristics of convex mirrors?**

All objects will have the same image characteristics regardless of object distance in convex mirrors. The characteristics are as follows:

- Located behind the convex mirror - A virtual image - An upright image - Reduced in size (i.e., smaller than the object)


 * What are the mirror equations for convex mirrors?**

The mirror equations for all mirrors are always the same. The difference being for convex mirrors, focal length is negative because it is behind the mirror and opposite the object.





=**CH 26**=

**Lesson 2: Color and Vision**
2A is summarized above.


 * What is the eye's response to visible light?**

The eye responds only to small portion of the electromagnetic spectrum referred to as the visible light spectrum. Light enters the eye through the pupil and then strikes the retina, which is lined with light sensing cells referred to as rods and cones. When certain wavelengths of light strike the cones of the retina, a chemical reaction happens that results in impulses being sent to the brain. There are three types of cones within the retina that are each sensitive to their respective wavelengths. The three cones are the red cones, blue cones, and green cones.






 * What are light absorption, reflection, and transmission?**

Different objects either absorb, reflect, or transit certain frequencies of light. How the object interacts with each frequency depends on the frequency of the light and that atoms that compose the object. Absorption occurs when the atoms vibrate at the same frequency as the incoming light. Reflection and transmission occur if the frequency of the light and atoms do not match. If an object absorbs all frequencies except one, then the object will be the same color as the color associated with that frequency. Chemicals that absorb one or more frequencies of light are called pigments.


 * What is color addition and subtraction?**

The primary colors of light are red, green, and blue. The mixing or addition of these primary colors in varying intensity can produce a wide range of other colors. The primary colors of light mixed together produce white light. This type of mixing is called color addition.

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. If a shirt absorbs blue light, and white light is shined on that shirt, then red and green light would be reflected. This process is called color subtraction, as blue light was subtracted from the original white light.


 * Why are skies blue and sunsets red?**

Atmospheric nitrogen and oxygen scatter violet light most easily, followed by blue light, green light, etc. So as white light (ROYGBIV) 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 without a significant alteration in their direction. This scattering of the higher frequencies of light illuminates the skies with light on the BIV end of the visible spectrum. Compared to blue light, violet light is most easily scattered by atmospheric particles. However, our eyes are more sensitive to light with blue frequencies. Thus, we view the skies as being blue in color. The appearance of the sun changes with the time of day. While it may be yellow during midday, it is often found to gradually turn color as it approaches sunset. This can be explained by light scattering. As the sun approaches the horizon line, sunlight must traverse a greater distance through our atmosphere. 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. The affect of a red sunset becomes more pronounced if the atmosphere contains more and more particles.

Lesson 1

 * What is the boundary behavior for waves on a rope?**

When the wave reaches the boundary, two things happen:

- 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.


 * How do light waves refract?**

When light travels from one medium to another medium, the light path bends. This refraction only occurs at a boundary.


 * What is the cause of refraction?**

The causes of refraction are twofold. Refraction will only occur if light hits the boundary at an angle (refraction will not occur perpendicularly) and if the speed changes at the boundary.


 * What is optical density?**

When an electromagnetic wave is traveling through a medium, its speed is dependent on the optical density of the medium. The 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.


 * What is the index of refraction?**

One indicator of the optical density of a material is the index of refraction of the material. Index of refraction values (represented by the symbol **n** ) are numerical index values that are expressed relative to the speed of light in a vacuum. The index of refraction value of a material is a number that indicates the number of times slower that a light wave would be in that material than it is in a vacuum.


 * What is the direction of bending?**

The direction of bending depends on whether the light ray is moving from a fast medium to slow medium or vice versa. In the former case, the light ray will bend toward the normal line. In the latter case, the light ray will bend away from the normal line at the boundary. No bending will occur if the medium doesn't change or if the index of refraction between two mediums stays the same.


 * What is the least time principle?**

The least time principle states that 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.

Lesson 2
**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 **

**Lesson 3**

 * What is total internal reflection?**

Total internal reflection is the reflection of the total amount of incident light at the boundary between two media. There are two requirements for TIR to occur:

- 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?**

The critical angle is the largest incident angle for which refraction can still occur. An incident angle greater than the critical angle will result in total internal reflection. Find the critical angle as follows:



**Lesson 4**

 * How is light dispersed by a prism?**

The separation of visible light into its different colors is called dispersion. Each color has a different wave frequency and different wave frequencies will bend different amounts depending on the optical density or index of refraction.


 * What is the angle of deviation?**

The amount of overall refraction caused by the passage of a light ray through a prism is often expressed in terms of the angle of deviation. 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. Colors of the visible light spectrum that have shorter wavelengths (BIV) will deviated more from their original path than the colors with longer wavelengths (ROY). The emergence of different colors of light from a triangular prism at different angles leads an observer to see the component colors of visible light separated from each other.




 * How is a rainbow formed?**

To view a rainbow, your back must be to the sun as you look at an approximately 40 degree angle above the ground into a region of the atmosphere with suspended droplets of water or even a light mist. Each individual droplet of water acts as a tiny prism that both disperses the light and reflects it back to your eye.


 * What is a mirage?**

A mirage is 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. As you drive down the roadway, there appears to be a puddle of water on the road several yards (maybe one-hundred yards) in front of the car.



**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: converging lens and diverging lens.

A converging lens is 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. A diverging lens is 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.



Similar to mirrors, lenses also have focal points and a point called 2F or double the focal point used as a reference point.




 * What are the rules of refraction for lenses?**

Converging:

- 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.
 * -** 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.

Diverging:

- 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.

Third Rule for Both Lenses:

- 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 lenses (converging)?**

Characteristics:

Case 1: the object is located //beyond// the 2F point -- //reduced, inverted, real, between F and 2F// Case 2: the object is located at the 2F point -- same size as object, inverted, real, at F Case 3: the object is located between the 2F point and the focal point (F) -- enlarged, inverted, real, beyond 2F 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) -- enlarged, upright, virtual, in front of the lens (between F' and 2F')



Ray Diagram:




 * What are the ray diagrams and image characteristics for lenses (diverging)?**

Characteristics:

In any situation, regardless of object distance, the image is always:

- located on the object's side of the lens - a virtual image - an upright image - reduced in size (i.e., smaller than the object)

Ray Diagram:




 * What are the mathematics of lenses?**

The equations for lenses are the same as those for mirrors. The focal length for a concave lens is negative.





**Lesson 6**

 * What is the anatomy of the eye?**




 * How does the eye form and detect images?**

The eye consists of a cornea (thin outer membrane), a lens attached to cilliary muscles, and a retina (inner surface equipped with nerve cells). These four parts of the eye are the most instrumental in the task of producing images that are discernible by the brain. In order to facilitate the ability to see, each part must enable the eye to refract light so that is produces a focused image on the retina. The lens of the eye is not where all the refraction of incoming light rays takes place. 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 lensis what explains the ability of the cornea to do most of the refracting of incoming light rays. The cornea-lens system produces an image of an object on the retinal surface.


 * What is accommodation?**

The ability of the eye to adjust its focal length is known as accommodation. Since a nearby object is typically focused at a further distance, the eye accommodates by assuming a lens shape that has a shorter focal length. This reduction in focal length will cause more refraction of light and serve to bring the image back closer to the cornea/lens system and upon the retinal surface. So for nearby objects, the cilliary muscles contract and squeeze the lens into a more convex shape.




 * What is farsightedness and how do you correct for 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. To correct for farsightedness the eye is assisted by the use of a converging lens. This converging lens will refract light before it enters the eye and subsequently decreases the image distance.


 * What is nearsightedness and how do you correct for it?**

Nearsightedness is the inability of the eye to focus on distant objects. Nearsightedness will result if the light from distant objects is refracted more than is necessary. Nearsightedness can be corrected by assisting the eye with a diverging lens. Since the nature of the problem of nearsightedness is that the light is focused in front of the retina, a diverging lens will serve to diverge light before it reaches the eye. This light will then be converged by the cornea and lens to produce an image on the retina.