Report the best value you have for the focal length of each lens, including the concave lens. Report any relationships that you have observed during the analysis, and comment on the difference between positive and negative lenses.

Using the lens equation (1), calculate the focal length of each lens or lens combination. Since you have found two focused positions for each lens, you should compute two values of focal length for each lens from the data. Average these two values. Compare, using percent difference, this average value with the value found by focusing a distant object. What do you notice about the object and image distances for the two positions of the same lens?

Repeat this procedure for each of the convex lenses at your station. Record the data for each lens in an organized manner for later analysis. Also, pick any two convex lens and carefully place them into a single lens holder. Repeat the procedures for measuring focal length for this lens combination. Finally, place the concave lens and the shortest focal length convex lens together in a lens holder, and measure the focal length of this combination.

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Measure the size of the grid object, and compute the magnification as the ratio of image size to object size for each set of data that you have. Compare this to the ratio of image distance to object distance (equation 2), using percent difference, for each data set. Look carefully at the two magnifications for the two positions of the same lens. What is the relationship between these magnifications?

When a beam of rays parallel to the principal axis of a lens impinges upon a converging lens, it is brought together at a point called the principal focus of the lens. The distance from the principal focus to the center of the lens is the focal length of the lens; the focal length is positive for a converging lens and negative for a diverging lens.

Negative focal lengthdiverging lens

When you have completed this experimental activity, you should be able to: (1) define focal length; (2) differentiate between positive and negative lenses; (3) measure focal length for a single thin lens and for combinations of thin lenses; and (4) distinguish between a real image and a virtual image.

Do concave mirrors havenegative focal length

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The numbers on binoculars tell you their strength (magnification) and their size (objective lens diameter).

There are several lenses at your work station. Two of them are double concave lenses, and the rest of them are double convex. Take one of the convex lenses and measure its focal length by focusing a distant object or light source on the screen. Use an object four or more meters from the lens to do this accurately. Measure the distance from the lens to the screen where the image is sharply focused as the focal length of the lens. Record the distance in a data table. Do the same for each of the convex lenses at your station.

Negative focal lengthreal or virtual

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Focal lengthof convex mirror is positive ornegative

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We thank Edmund Industrial Optics for their continued support of the Department of Physics here at Georgetown University.

When two thin lenses are in contact, the equivalent focal length of the combination may be measured experimentally by one of the above methods. It may also be calculated in terms of the individual focal lengths as:

focallength中文

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The relation between the object distance (p), the image distance (q), and the focal length (f) of a thin lens is given by the lens equation:

Most optical instruments in common usage have one or more lenses in them. Whether it is a microscope, a telescope, or even a simple magnifying glass, the crucial element is a lens. The formation of images by lenses is one of the most important studies in the field of optics. In particular, in this experiment you will measure the focal length of both positive and negative lenses, and examine a combination of thin lenses.

From the lens combination using the concave lens, calculate the focal length of the concave (negative) lens. The algebraic value from the computation comes out negative, which is why it is called a negative lens. Why could you not measure the focal length of this concave lens by itself?

The magnification produced by a lens (the linear magnification) is defined as the ratio of the height of the image to the height of the object. This can be shown, by the use of geometry for similar triangles, to be equal to the ratio of the image distance to the object distance. Thus

FOV tofocal length

Negative focal lengthmirror

where feq is the equivalent focal length of the lens combination, and f1 and f2 are the focal lengths of the two lenses that make the combination.

Edmund Industrial Optics has supported the Department of Physics in innumerable and impactful ways over their many years of philanthropy, providing greater opportunity for our students and professors to explore research opportunities. Among items that Edmund’s support has afforded the Department is specialized optical equipment that has been used in eight different faculty research labs, the Georgetown Nanoscience and Microtechnology Laboratory (GNuLab), and the Institute for Soft Matter Synthesis and Metrology shared research facility.

The optical equipment has been used to develop systems for optical characterization of materials and measurements of interactions of light with matter. For example, components received by the Van Keuren lab are being used to develop a novel instrument for measuring molecular interactions in solution. The equipment not only bolsters our research capabilities, but is also used in teaching labs for upper level undergraduate course in optics.

With the object and screen still fixed in the same positions, move the lens back and forth along the optical bench until another position is found where sharp image is formed on the screen. Record the object and image distances for this location, as well as the image size.

Focal length

Now you will determine the focal length of each lens by a different method, using the lens equation (1). Take the convex lens with the shortest focal length, and place it in a lens holder on the optical bench. Place the light source and grid object at one end of the optical bench, and place the white cardboard screen at a distance of about 5 times the focal length of the lens from the object, with the lens between the object and screen. Leave the object and screen fixed, and move the lens along the bench until a sharp image of the grid object forms on the screen. Measure the distance between the object and the lens, and between the lens and the screen, and record these in a data table. Also, measure the size of the image on the screen.

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A concave lens by itself cannot form a real image on a screen, since it is a diverging lens. Hence, a different method must be used for measuring its focal length. This is done by placing the negative lens in contact with a positive lens of shorter focal length whose focal length is known. The equivalent focal length of the combination can be measured experimentally, and the focal length of the negative lens computed using equation (3).

The principal focal length of a converging lens may be determined by forming an image of a very distant object on a screen and measuring the distance from the lens to the screen. This distance will be the focal length, since rays of light from a very distant object are very nearly parallel. A more accurate method of determining the focal length of a positive lens is to measure the image distance corresponding to a suitable and known object distance, and to calculate the focal length from the lens equation (1).

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Edmund Industrial Optics, Inc., formerly Edmund Scientific Company, has been a generous supporter of Georgetown University through two generations of Hoyas: Robert M. Edmund (B’70), his wife, Anne Gwynne Edmund, and daughters Nicole Anne Edmund (B’90), Genvieve Anne Edmund (N’93), and Marisa Anne Edmund (B’98).