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Magnificationformula biology

b. To get an image magnified by a factor of ten, we again solve Equation \ref{eq13} for \(f\), but this time we use \(M=10\). The result is

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We have seen that, when an object is placed within a focal length of a convex lens, its image is virtual, upright, and larger than the object (see part (b) of this Figure). Thus, when such an image produced by a convex lens serves as the object for the eye, as shown in Figure \(\PageIndex{2}\), the image on the retina is enlarged, because the image produced by the lens subtends a larger angle in the eye than does the object. A convex lens used for this purpose is called a magnifying glass or a simple magnifier.

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Download the brochure to learn more about the development of our Fresnel lenses, lens specifications, and details on how to order the lens you need.

The apparent size of an object perceived by the eye depends on the angle the object subtends from the eye. As shown in Figure \(\PageIndex{1}\), the object at \(A\) subtends a larger angle from the eye than when it is position at point \(B\). Thus, the object at \(A\) forms a larger image on the retina (see \(OA′\)) than when it is positioned at \(B\) (see \(OB′\)). Thus, objects that subtend large angles from the eye appear larger because they form larger images on the retina.

Inserting Equation \ref{eq34} into Equation \ref{eq10} gives us the final equation for the angular magnification of a magnifying lens:

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Microscope

\[\begin{align} M&= \left(−\dfrac{d_i}{d_o}\right)\left(\dfrac{25\,cm}{L}\right) \\[4pt] &=−d_i\left(\dfrac{1}{f}−\dfrac{1}{d_i}\right)\left(\dfrac{25\,cm}{L}\right) \\[4pt] &= \left(1−\dfrac{d_i}{f}\right)\left(\dfrac{25\,cm}{L}\right) \label{eq10} \end{align} \]

Today's modern computer-controlled machining methods can be used to cut the surface of each cone precisely to bring all paraxial rays into focus at exactly the same point, avoiding spherical aberration. Better still, newer optical manufacturing methods can be used to cut each refracting surface in the correct aspheric contour (rather than as a conical approximation to this contour), thus avoiding even the width of the groove (typically 0.1 to 1 mm) as a limit to the sharpness of the focus. Even though each groove or facet brings light precisely to a focus, the breaking up the wavefront by the discontinuous surface of a Fresnel lens degrades the visible image quality. Except in certain situations, Fresnel lenses are usually not recommended for imaging applications in the visible light region of the spectrum.

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a. The required linear magnification is the ratio of the desired image diameter to the diamond’s actual diameter (Equation \ref{eq15}). Because the jeweler holds the magnifying lens close to his eye and the image forms at his near point, the linear magnification is the same as the angular magnification, so

From Figure \(\PageIndex{1b}\), we see that the absolute value of the image distance is \(|d_i|=L−ℓ\). Note that \(d_i<0\) because the image is virtual, so we can dispense with the absolute value by explicitly inserting the minus sign:

which shows that the greatest magnification occurs for the lens with the shortest focal length. In addition, when the image is at the near-point distance and the lens is held close to the eye (\(ℓ=0\)), then \(L=d_i=25\,cm\) and Equation \ref{eq12} becomes

Fresnel Technologies, Inc. specializes in the design and manufacturing of molded plastic Fresnel lenses, molded polymer optics in general, and infrared-transmitting optical materials. We offer design assistance, diamond machining, prototyping, tooling, and production. Stock or custom, we’re your optics partner.

Convexlens

Fresnel Technologies makes a variety of stock Fresnel and related optical components to meet your needs. We can also design and construct custom Fresnel lenses and polymer optics  as requested. Our Fresnel items fall into a number of categories, but they are all made from polymer materials. Generally, our engineers design these components with thicknesses under 1/4" (6 mm) with a stepped surface.

Fresnel Technologies, Inc. specializes in the design and manufacturing of molded plastic Fresnel lenses, molded polymer optics in general, and infrared-transmitting optical materials. We offer design assistance, diamond machining, prototyping, tooling, and production. Stock or custom, we’re your optics partner.

By comparing Equations \ref{eq13} and \ref{eq15}, we see that the range of angular magnification of a given converging lens is

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A jeweler wishes to inspect a 3.0-mm-diameter diamond with a magnifier. The diamond is held at the jeweler’s near point (25 cm), and the jeweler holds the magnifying lens close to his eye.

Fresnel Technologies, Inc. specializes in the design and manufacturing of molded plastic Fresnel lenses, molded polymer optics in general, and infrared-transmitting optical materials. We offer design assistance, diamond machining, prototyping, tooling, and production. Stock or custom, we’re your optics partner.

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The resulting magnification is simply the ratio of the near-point distance to the focal length of the magnifying lens, so a lens with a shorter focal length gives a stronger magnification. Although this magnification is smaller by 1 than the magnification obtained with the image at the near point, it provides for the most comfortable viewing conditions, because the eye is relaxed when viewing a distant object.

Magnificationformula

We need to determine the requisite magnification of the magnifier. Because the jeweler holds the magnifying lens close to his eye, we can use Equation \ref{eq13} to find the focal length of the magnifying lens.

Section Summary · A diffraction grating is a large collection of evenly spaced parallel slits that produces an interference pattern similar to but sharper than ...

Magnifying Glass

While spherical aberration is caused by a difference in focused point, coma is caused by a difference in magnification. A point image such as a star tails ...

\[\underbrace{ M=\dfrac{θ_{image}}{θ_{object}}=\dfrac{h_i(25cm)}{Lh_o}}_{\text{angular magnification}} . \label{angular magnification} \]

where \(m\) is the linear magnification (Equation \ref{mag}) previously derived for spherical mirrors and thin lenses. Another useful situation is when the image is at infinity (\(L=\infty\)). Equation \ref{eq12} then takes the form

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Note that a greater magnification is achieved by using a lens with a smaller focal length. We thus need to use a lens with radii of curvature that are less than a few centimeters and hold it very close to our eye. This is not very convenient. A compound microscope, explored in the following section, can overcome this drawback.

To account for the magnification of a magnifying lens, we compare the angle subtended by the image (created by the lens) with the angle subtended by the object (viewed with no lens), as shown in Figure \(\PageIndex{1a}\). We assume that the object is situated at the near point of the eye, because this is the object distance at which the unaided eye can form the largest image on the retina. We will compare the magnified images created by a lens with this maximum image size for the unaided eye. The magnification of an image when observed by the eye is the angular magnification \(M\), which is defined by the ratio of the angle \(θ_{image}\) subtended by the image to the angle \(θ_{object}\) subtended by the object:

by SB Ali Reza · 2023 · Cited by 8 — Free-space optical communications (FSO) is a line of sight communication method that provides unguided wireless optical data in free space. The ...

magnification中文

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Note that all the quantities in this equation have to be expressed in centimeters. Often, we want the image to be at the near-point distance (e.g., \(L=25\,cm\)) to get maximum magnification, and we hold the magnifying lens close to the eye (\(ℓ=0\)). In this case, Equation \ref{eq12} gives

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Consider the situation shown in Figure \(\PageIndex{1b}\). The magnifying lens is held a distance \(ℓ\) from the eye, and the image produced by the magnifier forms a distance \(L\) from the eye. We want to calculate the angular magnification for any arbitrary \(L\) and \(ℓ\). In the small-angle approximation, the angular size \(θ_{image}\) of the image is \(h_i/L\). The angular size \(θ_{object}\) of the object at the near point is \(θ_{object}=h_o/25\,cm\). The angular magnification is then