^_^LENS^_^

lens is a device that causes light to either converge and concentrate or to diverge. It is usually formed from a piece of shaped glass or plastic. Analogous devices used with other types of electromagnetic radiation are also called lenses: for instance, a microwave lens can be made from paraffin wax.

LENS CONSTRUCTION

Most lenses are spherical lenses: lenses whose surfaces have spherical curvature, that is, the front and back surfaces of the lens can each be imagined to be part of the surface of a sphere. Each surface can be convex (bulging outwards from the lens), concave (depressed into the lens), or planar (flat). The line joining the centres of the spheres making up the lens surfaces is called the axis of the lens; in almost all cases the lens axis passes through the physical centre of the lens.

Types of lenses
Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (also called double convex, or just convex) if both surfaces are convex, likewise, a lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave, and in this case if both curvatures are equal it is a meniscus lens. (Sometimes, meniscus lens can refer to any lens of the convex-concave type).

If the lens is biconvex or plano-convex, a collimated or parallel beam of light travelling parallel to the lens axis and passing through the lens will be converged (or focused) to a spot on the axis, at a certain distance behind the lens (known as the focal length). In this case, the lens is called a positive or converging lens.


If the lens is biconcave or plano-concave, a collimated beam of light passing through the lens is diverged (spread); the lens is thus called a negative or diverging lens. The beam after passing through the lens appears to be emanating from a particular point on the axis in front of the lens; the distance from this point to the lens is also known as the focal length, although it is negative with respect to the focal length of a converging lens.


If the lens is convex-concave (a meniscus lens), whether it is converging or diverging depends on the relative curvatures of the two surfaces. If the curvatures are equal, then the beam is neither converged nor diverged.

Lensmaker's equation
The focal length of a lens in air can be calculated from the lensmaker's equation.

where:
f is the focal length of the lens,
n is the refractive index of the lens material,
R1 is the radius of curvature of the lens surface closest to the light source,
R2 is the radius of curvature of the lens surface farthest from the light source, and
d is the thickness of the lens (the distance along the lens axis between the two surface vertices).

Sign convention of lens radii R1 and R2

The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article if R1 is positive the first surface is convex, and if R1 is negative the surface is concave. The signs are reversed for the back surface of the lens: if R2 is positive the surface is concave, and if R2 is negative the surface is convex. If either radius is infinite, the corresponding surface is flat.

Thin lens equation
If d is small compared to R1 and R2, then the thin lens approximation can be made. For a lens in air, f is then given by

The focal length f is positive for converging lenses, negative for diverging lenses, and infinite for meniscus lenses. The value 1/f is known as the optical power of the lens, and so meniscus lenses are said to have zero power. Lens power is measured in dioptres, which are units equal to inverse meters (m−1).
Lenses have the same focal length when light travels from the back to the front as when light goes from the front to the back, although other properties of the lens, such as the aberrations are not necessarily the same in both directions.

So.. for the past 2 weeks, here we are again.. to post some of our requirments for our BLOG.. which is a part of our project.. Mr. Mendoza, said that we must have these following posts in our blog: 1. CONCAVE and CONVEX MIRRORS with their explanation and diagrams

2. LENSES with their explanation and diagrams
3. EYE and CAMERA

I. CONCAVE and CONVEX MIRRORS

Terms and Definition:

1. 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.

2. 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.

3. 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.

4. 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.

5. The distance from the vertex to the center of curvature is known as the radius of curvature (abbreviated by "R").

6. The distance from the mirror to the focal point is known as the focal length (abbreviated by "f").

CONCAVE:

The simpler method relies on two simple rules of reflection for concave mirrors. They are:
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.
These two rules of reflection are illustrated in the diagram below.

The method of drawing ray diagrams for concave mirror is described below. The description is applied to the task of drawing a ray diagram for an object located beyond the center of curvature (C) of a concave mirror.

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.

2. Once these incident rays strike the mirror, reflect them according to the two rules of reflection for 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 which 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.

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. (See note below.)

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 which 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.CONVEX:

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.

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.
These two rules will be used to construct ray diagrams. A ray diagram is a tool used to determine the location, size, orientation, and type of image formed by a mirror. Ray diagrams for concave mirrors were drawn in Lesson 3. In this lesson, we will see a similar method for constructing ray diagrams for convex mirrors.
The method of drawing ray diagrams for convex mirrors is described below.

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 travels towards the focal point on the opposite side of the mirror; this ray will strike the mirror before reaching the focal point; stop the ray at the point of incidence with 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.

2. Once these incident rays strike the mirror, reflect them according to the two rules of reflection for convex mirrors.
The ray that travels towards the focal point will reflect and travel parallel to the principal axis. Use a straight edge to accurately draw its path. The ray which traveled parallel to the principal axis on the way to the mirror will reflect and travel in a direction such that its extension passes through the focal point. Align a straight edge with the point of incidence and the focal point, and draw the second reflected ray. Place arrowheads upon the rays to indicate their direction of travel. The two rays should be diverging upon reflection.

3. Locate and 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. Since the two reflected rays are diverging, they must be extended behind the mirror in order to intersect. Using a straight edge, extend each of the rays using dashed lines. Draw the extensions until they intersect. The point of intersection is the image point of the top of the object. Both reflected rays would appear to diverge from this point. If your were to draw a third pair of incident and reflected rays, then the extensions of 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 appear to diverge from 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.

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 which is formed by the convex 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 complete image can be filled in.

Some students have difficulty understanding how the entire image of an object can be deduced once a single point on the image has been determined. If the object is merely a vertical object (such as the arrow object used in the example below), then the process is easy. The image is merely a vertical line. This is illustrated in the diagram below. In theory, it would be necessary to pick each point on the object and draw a separate ray diagram to determine the location of the image of that point. That would require a lot of ray diagrams as illustrated in the diagram below.
Fortunately, a shortcut exists. If the object is a vertical line, then the image is also a vertical line. For our purposes, we will only deal with the simpler situations in which the object is a vertical line which has its bottom located upon the principal axis. For such simplified situations, the image is a vertical line with the lower extremity located upon the principal axis.

...So finally.. we are now finished in our video clip for our project.. tsk3.. but we still need to edit it so that we could finally finished and try to pass it early.. nd i want to thank my groupmates.. Jhonnet Galit, Alyssa Lapira, Vernisse Celiz, SETH REVELO and BON JOVI REGALA.. haha.. So.. we will try to finish our project this week.. Yeah!!!.. that's ol for today.. ^_^

Yess!!!... Finally!!... Drought is over... The longtest is over.. nd ol of us failed.. How Sad :(.. But i will do my best for the periodic to catch up with my grades.. DAmn it..

http://www.geocities.com/moskimen/links/downloads.htm... Wahu.. So this is the site that sir Mendoza gave us to create a paper... Hehe... Ok... So... For this week... I will be busy because of our paper and our project...

Yayayay...... Haha... Hayy... I'm still not finished with editing my blog because i'm too bored to do it... Ahehe... Maybe i'll just find the time when i can really edit it... And... I'm still thinking of what song should rily fit for our project... Maybe i'll find some songs later and i will make it na... So that we will finish our project early... Hehe... *And here are the vectors that we learned all about*... ^_^

Basic Vector Operations

Both a magnitude and a direction must be specified for a vector quantity, in contrast to a scalar quantity which can be quantified with just a number. Any number of vector quantities of the same type (i.e., same units) can be combined by basic vector operations.

Graphical Method:

Adding two vectors A and B graphically can be visualized like two successive walks, with the vector sum being the vector distance from the beginning to the end point. Representing the vectors by arrows drawn to scale, the beginning of vector B is placed at the end of vector A. The vector sum R can be drawn as the vector from the beginning to the end point.
The process can be done mathematically by finding the components of A and B, combining to form the components of R, and then converting to polar form.

Component Method:

Finding the components of vectors for vector addition involves forming a right triangle from each vector and using the standard triangle trigonometry.
The vector sum can be found by combining these components and converting to polar form.

Yesss!!.... Hahaha.. Finally..Yesterday, we all passed to our test in Physics.. It's all about History Of Light which is to easy because you don't need the use of your Sci cal.. But to listen only to Sir Mendoza.. Haha.. Luckly I got 9/10... Which is good for now.. But i'll make sure next time that i will show to Sir mendoza that I can perfect his test... Hahahaha