# Lenses and Focal Points

Lenses are apparatus made of glass or other transparent material that are used to converge or diverge light rays from their initial path. They are often identified with their focal lengths. The focal length of the lens is the distance (mostly in cm) from the focal point its center. The focal point dictates the position at which the rays of light converge, or seem to converge, after they are either diverged or converged by a lens (“Reading on Refraction”, n.d.).

All optical elements, mirrors and lenses, have their own unique focal length. This focal length is the defining characteristic of the lenses.

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The focal point should always be determined using parallel rays. If light is already converging when it meets the curved surface of the lenses, the focal point seems to move closer. If the light is diverging, the focal point moves further from the lenses. This focal point is unacceptable due to its variability (“Reading on Refraction”, n.d.).

Lenses may either be convex or concave. Convex lenses are similar to the one used in the diagram above. They have surfaces that bulge outwards. Their focal length is positive. A positive focal length is obtained when the image is obtained on the side opposite the object. A concave lens has surfaces that bulge inwards. Its focal length is negative. A negative focal length implies that object and image appear on the same side. The image produced by a concave lens can be seen but cannot be placed on a screen or a surface and is, therefore, known as a virtual image. A concave lens disperses light as shown below (“Reading on Refraction, part 2”, n.d.).

The focal point, as shown above is the position at which the beams of light would converge. It is determined by extending the rays of light so that they meet. The extended parts of the light rays are usually drawn using dotted lines to differentiate them from the real parts of the rays (“Reading on Refraction, part 2”, n.d.).

A convex lens forms an image on the other side of the lens. It is usually located on the opposite side with the object. The image can be placed on a screen or sheet of paper. For this purpose, the model is said to be real. Real images can, therefore, be both seen and formed on a piece of paper (“Reading on Refraction”, n.d.).

Real and virtual images may also be produced in mirrors. The images created in flat mirrors and convex mirrors are virtual images. They are created as a consequence of the failure by the rays involved to converge practically. On the flat mirror, rays fail to meet since they are parallel to each other. In the convex mirror, rays fail to meet as a result of dispersion of these rays in different directions. The images formed on the convex and the flat mirrors are produced on the other side of the mirrors unlike in the case of concave lens (“Reading on Refraction, part 2”, n.d.).

Concave mirrors form real images. This image is created on the same region with the object. When the rays hit the face of the mirror, they are reflected at acute angles so that they all converge at a central point on the side of the object (“Reading on Refraction, part 3”, n.d.).

The meeting point is the mirrors’ focal point. Real images are usually inverted while virtual images are upright (“Reading on Refraction, part 3”, n.d.).

Ray tracing

Ray tracing is a method that is use to determine the object position. For this to be done, one must know the focal point. The knowledge of ray tracing is usually used when determining the best pairs of spectacles that should be worn by an individual. Without this knowledge, the process would be so tiresome and expensive.

Convex lenses

The following facts are always considered when doing this on a convex lens. First, the light that emanates from the object bottom, typically at the optical axis of the lens runs along a straight line and is not sidetracked by the lens. The light at the top of the object runs parallel to that which is at the middle up to the point where it hits the lens. Once it hits the lens, it is bent in such a fashion that it cuts through the focal point on the image region of the lenses. Third, when the light that goes through the focal point in the region where the object is situated hits the surface of the lens, it is refracted so that it runs conforming with the optical axis in the image side. There are five probable situations in the case of the convex lens (“Ray Diagrams for Lenses”, n.d.).

First, the object may be placed beyond two times the focal length away from the mirror. In that case, the image is always formed at appoint between the focal length, F, and 2F. The image is always inverted and reduced in size. It is also, as stated earlier, a real image. This can be represented as shown below (“Reading on Refraction, part 3”, n.d.).

Secondly, the object may be placed at point 2F. In that case, the image is produced at the point 2F on the opposite region of the lenses. The image is the same size with the object and is inverted. The image is also real and can be projected on a piece of paper (“Ray Diagrams for Lenses”, n.d.).

Thirdly, the object may be placed between 2F and the focal point. In that case, the object formed is always formed past the focal point in the reverse side of the lens, is inverted, real and larger than the object (“Ray Diagrams for Lenses”, n.d.).

Fourthly, the object may be placed on the focal point. In such a case, no image is formed. When light rays pass through the convex mirror from this point, they are neither converged nor diverged. Since they are parallel to each other, no image is formed (“Ray Diagrams for Lenses”, n.d.).

Fifth, the object may be placed between the focal length and the lens. In that case, the image formed is virtual, erect, and on the same region with the object. The image distance is always longer than the object distance. Since it is virtual, it cannot be formed on a screen and its location is determined by extending the rays to the object side to get where they meet.

Concave lenses

For a concave lens, the image distance also determines the location, orientation, size and type of image formed. There are five possible scenarios for lenses (“Ray Diagrams for Lenses”, n.d.).

When an object is positioned at a point at infinity, it forms an image on the focal point, virtual, erect and diminished.

For an object positioned at the point 2F from the lens center, the image is formed between the lens and f, is upright, reduced and inverted (“Ray Diagrams for Lenses”, n.d.).

For an object located at focal point, the image is produced at a point between the focal point and the lens and is upright, virtual, formed between the lens and f, and reduced. An image formed between the lenses and the focal point is erect, virtual, formed between the lens and the focal point, and reduced.

Therefore, in the case of concave lenses, the image distance is always smaller than the object distance. The image is also always reduced (“Ray Diagrams for Lenses”, n.d.).

Images formed this way are always, as shown above between the object and the lens.

Fresnel lenses

Fresnel lenses were discovered in an attempt to lower the cost of big lenses. They are made by cutting the inside part of the lenses so as to remain with only one curved surface, they are cheaper and lighter than ordinary lenses. They can also have the same magnification power as that of glass lenses. The lenses however give poor images due to the material used for making the lenses. The lenses are made of plastic (“Reading on Fresnel Lenses”, n.d.).

Works Cited

“Converging Lenses – Ray Diagrams.” The Physics Classroom. N.p., n.d. Web. 19 June 2014.

“Ray Diagrams for Lenses.” N.p., Web. 19 June 2014. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/raydiag.html

“Reading on Fresnel Lenses.” Arizona State University | A top ranked research university | ASU. N.p., n.d. Web. 19 June 2014.

“Reading on Refraction, part 2.” Arizona State University | A top ranked research university | ASU. N.p., n.d. Web. 19 June 2014.

“Reading on Refraction, part 3.” Arizona State University | A top ranked research university | ASU. N.p., n.d. Web. 19 June 2014.

“Reading on Refraction.” Arizona State University | A top ranked research university | ASU. N.p., n.d. Web. 19 June 2014.

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