Saturday, August 11, 2007
If a piece of glass or other transparent material takes on the appropriate shape, it will be capable of taking parallel rays of incident light and either converging them to a point or appear to diverge them from a point. Such a piece of glass is referred to as a lens.
A lens is merely a carefully ground or molded piece of transparent material which refracts light rays in such as way as to form an image. Lenses can be thought of as a series of tiny refracting lenses, each of which refracts light to produce their own image. When these prisms act together, they produce a bright enough image focused at a point.
There are a variety of types of lenses. Lenses differ from one another in terms of their shape and the materials from which they are made. Our focus will be upon lenses which are symmetrical across their horizontal axis - known as the principal axis. In this unit, we will categorize lenses as converging lenses and diverging lenses. A converging lens is a lens which converges rays of light which are traveling parallel to its principal axis. Converging lenses can be identified by their shape; they are thicker across their middle and thinner at their upper and lower edges. A diverging lens is a lens which diverges rays of light which are traveling parallel to its principal axis. Diverging lenses can also be identified by their shape; they are thinner across their middle and thicker at their upper and lower edges.
A double convex lens is symmetrical across both its horizontal and vertical axis. Each of the lens' two faces can be thought of as originally being part of a sphere. The fact that a double convex lens is thicker across its middle is an indicator that it will converge rays of light which travel parallel to its principal axis. A double convex lens is a converging lens. A double concave lens is also symmetrical across both its horizontal and vertical axis. The two faces of a double concave lens can be thought of as originally being part of a sphere. The fact that a double concave lens is thinner across its middle is an indicator that it will diverge rays of light which travel parallel to its principal axis. A double concave lens is a diverging lens.
If a symmetrical lens is thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror in the exact center of the lens. This imaginary line is known as the principal axis. A lens also has an imaginary vertical axis which bisects the symmetrical lens in two. As mentioned above, light rays incident towards either face of the lens and traveling parallel to the principal axis will either converge or diverge. If the light rays converge (as in a converging lens), then they will converge to a point. This point is known as the focal point of the converging lens. If the light rays diverge(as in a diverging lens), then the diverging rays can be traced backwards until they intersect at a point. This point is known as the focal point of a diverging lens. The focal point is denoted by the letter F on the diagrams below. Note that each lens has two focal points - one on each side of the lens. Unlike mirrors, lenses can allow light to pass through either face, depending on where the incident rays are coming from. Subsequently, every lens has two possible focal points. The distance from the mirror to the focal point is known as the focal length .Technically, a lens does not have a center of curvature. However a lens does have an imaginary point which we refer to as the 2F point. This is the point on the principal axis which is twice as far from the vertical axis as the focal point is.
PICTURES TO FOLLOW!
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If a concave mirror is thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror. This line is known as the principal axis. The point in the center of sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram below. The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A in the diagram below. The vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is a point known as the focal point; the focal point is denoted by the letter F in the diagram below. The distance from the vertex to the center of curvature is known as the radius of curvature (abbreviated by "R"). The radius of curvature is the radius of the sphere from which the mirror was cut. Finally, the distance from the mirror to the focal point is known as the focal length (abbreviated by "f"). Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature.
The focal point is the point in space at which light incident towards the mirror and traveling parallel to the principal axis will meet after reflection. The diagram at the right depicts this principle. In fact, if some light from the Sun was collected by a concave mirror, then it would converge at the focal point. Because the Sun is such a large distance from the Earth, any light rays from the Sun which strike the mirror will essentially be traveling parallel to the principal axis. As such, this light should reflect through the focal point. Perhaps you remember the outdoors demonstration in which a pencil was engulfed in flames in a matter of seconds when placed at the focal point of the demonstration mirror. In the demonstration, whatever light from the Sun which hit the mirror was focused at the point where the pencil was. To the surprise of many, the heat was sufficient to ignite the pencil. Wow!
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convex mirror was described as a portion of a sphere which had been sliced away. If the outside of the sphere is silvered such that it can reflect light, then the mirror is said to be convex. The center of that original sphere is known as the center of curvature (C) and the line which passes from the mirror's surface through the sphere's center is known as the principal axis. The mirror has a focal point (F) which is located along the principal axis, midway between the mirror's surface and the center of curvature. Note that the center of curvature and the focal point are located on the side of the mirror opposite the object - behind the mirror. Since the focal point is located behind the convex mirror, such a mirror is said to have a negative focal length value.
A convex mirror is sometimes referred to as a diverging mirror due to its ability to take light from a point and diverge it. The diagram at the right shows four incident rays emanating from a point and incident towards a convex mirror. These four rays will each reflect according to the law of reflection. After reflection, the light rays diverge; subsequently they will never intersect on the object side of the mirror. For this reason, convex mirrors produce virtual images which are located somewhere behind the mirror.
Throughout this unit on Reflection and the Ray Model of Light, the definition of an image has been given. An image is the location in space where it appears that light diverges from. Any observer from any position who is sighting along a line at the image location will view the object as a result of reflected light; each observer sees the image in the same location regardless of the observer's location. As the observer sights along a line, a ray of light is reflecting off the mirror to the observer's eye. Thus, the task of determining the image location of an object is to determine the location where reflected light intersects. The diagram below shows an object placed in front of a convex mirror. Several rays of light emanating from the object are shown approaching the mirror and subsequently reflecting. Each observer must sight along the line of the reflected ray to view the image of the object. Each ray is extended backwards to a point of intersection - this point of intersection of all extended reflected rays indicates the image location of the object.
The image in the diagram above is a virtual image. Light does 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. The fact that all the reflected light from the object appears to diverge from this location in space means that any observer would view a replica or reproduction when sighting along a line at this location.
Of course to determine the image location, only a pair of incident and reflected rays need to be drawn. It is customary to select the pair of rays which are easiest to draw. Of the five pairs of incident and reflected rays in the diagram above, two correspond to the rays which are customarily drawn. In fact, they may closely resemble the two rays which were used in concave mirror ray diagrams. Recall from Lesson 3 that there were two rules of reflection for concave mirrors. They are:
Any incident ray traveling parallel to the principal axis on the way to a concave mirror will pass through the focal point upon reflection.
Any incident ray passing through the focal point on the way to a concave mirror will travel parallel to the principal axis upon reflection.
The revised rules can be stated as follows:
Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect in 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.
PICTURES TO FOLLOW
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Last tuesday we checked our LONG TEST II and the score was just good but not enough for me to pass....because the passing is 40 and my score is only 32..but i am still happy because i dont know that i will that score in that test..thanks for the problem solving...=)
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Saturday, August 4, 2007
this is my latest post after several weeks...
for the past long test:
I'm so happy that my parents was not called beacaused i hit the passing mark..but mr. mendoza included the next quizzes and long test(on monday) with the computation for those whose parents will be called and join the FAMILY DAY..sadly, my past quizzes were a littlle bit low and i am afraid that i might be included to the list of call parents.. but i will not lose hope, babawi na lng sa long test haha..=)
i am getting a little bit confused with the signs (+,-) in computing for the unknown in a lens type of mirror. I don't know when to make my unknown + or -. i wish that i could understand it before the long test..
I hope that i would pass the long test on monday....=)s
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Wednesday, July 11, 2007
ToMoRROW IS THe DAy.....HAve to Study, STudy And STudy
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Saturday, June 30, 2007
1.analyze the problem
2.make a convenient scale
3.draw the first vector
4.from the head of the first vector, connect the tail of the next vector, and so on
5.to get the resultant, close the given vectors from the head of the last to the point of origin
6.measure using the scale
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