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.

The second type of vignetting is natural vignetting, which occurs as a result of the angle at which the light coming into your camera, through the lens, ...

A C mount is a type of lens mount commonly found on 16 mm movie cameras, closed-circuit television cameras, machine vision cameras and microscope phototubes.

Some TV lenses lack provision to focus or vary the aperture, so may not operate properly with film cameras. Also, some TV lenses may have bits that protrude behind the mount far enough to interfere with the shutter or reflex finder mechanisms of a film camera.

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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.

Convexlens

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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.

Opticallens

Although C-mount lenses have a back focal distance far too short to be used with 35 mm film SLRs or any existing digital SLR, they can be mounted on interchangeable-lens mirrorless digital cameras such as the Micro Four Thirds used by Olympus and Panasonic. However, the vast majority of C-mount lenses produce an image circle too small to effectively cover the entire sensor which has approximately 22 mm diagonal, this produces vignetting.[1] The Nikon 1 series and the Pentax Q series can use C-mount lenses without vignetting.

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Depending on the format, the design of the lens and its performance will differ considerably. For example, for the 4/3 format, a 12 mm lens is a wide-angle lens and will have a retrofocus design. For the 2/3-inch format, a 12 mm lens is "normal" and can have a simple and fast double Gauss layout. For the 1/3-inch format, a 12 mm lens is long and can have a telephoto design.

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:

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

Magnificationformula

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

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.

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Magnificationformula biology

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

Microscope

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

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

magnification中文

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

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

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

Merely to say that a lens is "C-mount" says very little about the lens's intended use. C-mount lenses have been made for many different formats. C-mount lenses are built for the 8 mm and 16 mm film formats and the 1/3", 1/2", 2/3", 1", and 4/3" video formats, which corresponds to a range of image circles approximately from 5 to 22 mm in diameter.

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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C mount was created by Bell & Howell for their Filmo 70 cine cameras.[2] The earliest Filmos had slightly different mounts, known as A mount, and B mount. C mount was found on Filmo 70 cameras with serial numbers 54090 and higher,[3] probably from about 1926. Soon after, other camera manufacturers adopted the same mount, and it became a de facto standard for 16 mm cine cameras.

CS-mount has a flange focal distance of 12.526 millimetres (0.4931 in),[4][5] compared to 17.526 millimetres (0.6900 in) for a C mount, but is otherwise the same as C-mount, including the fact that lenses for many different formats are made for it. CS-mount lenses are built for the smaller formats, 1/2 inch and down.

Telephotolens

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

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:

Magnifying Glass

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.

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

C-mount lenses provide a male thread, which mates with a female thread on the camera. The thread is nominally 1 inch (25.4 mm) in diameter, with 32 threads per inch (0.794 mm pitch), designated as "1-32 UN 2A" in the ANSI B1.1 standard for unified screw threads. The flange focal distance is 17.526 millimetres (0.6900 in) for a C mount.

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