Magnification

Some optical instruments provide visual aid by magnifying small or distant subjects. • A magnifying glass, which uses a positive (convex) lens to make things look bigger by allowing the user to hold them closer to their eye. • A telescope, which uses its large objective lens or primary mirror to create an image of a distant object and then allows the user to examine the image closely with a smaller eyepiece lens, thus making the object look larger. • A microscope, which makes a small object appear as a much larger image at a comfortable distance for viewing. A microscope is similar in layout to a telescope except that the object being viewed is close to the objective, which is usually much smaller than the eyepiece. • A slide projector, which projects a large image of a small slide on a screen. A photographic enlarger is similar. • A zoom lens, a system of camera lens elements for which the focal length and angle of view can be varied. ==Size ratio (optical magnification)==

Optical magnification is the ratio between the apparent size of an object (or its size in an image) and its true size, and thus it is a dimensionless number. Optical magnification is sometimes referred to as "power" (for example "10× power"), although this can lead to confusion with optical power. Linear or transverse magnification For real images, such as images projected on a screen, size means a linear dimension (measured, for example, in millimeters or inches). Angular magnification For optical instruments with an eyepiece, the linear dimension of the image seen in the eyepiece (virtual image at infinite distance) cannot be given, thus size means the angle subtended by the object at the focal point (angular size). Strictly speaking, one should take the tangent of that angle (in practice, this makes a difference only if the angle is larger than a few degrees). Thus, angular magnification is given by M_A=\frac{\tan \varepsilon}{\tan \varepsilon_0}\approx \frac{\varepsilon}{ \varepsilon_0} where \varepsilon_0 is the angle subtended by the object at the front focal point of the objective and \varepsilon is the angle subtended by the image at the rear focal point of the eyepiece. For example, the mean angular size of the Moon's disk as viewed from Earth's surface is about 0.52°. Thus, through binoculars with 10× magnification, the Moon appears to subtend an angle of about 5.2°. By convention, for magnifying glasses and optical microscopes, where the size of the object is a linear dimension and the apparent size is an angle, the magnification is the ratio between the apparent (angular) size as seen in the eyepiece and the angular size of the object when placed at the conventional closest distance of distinct vision: from the eye. where black dimensions are real, the greys are virtual. ==By instrument==

Single lens The linear magnification of a thin lens is M = {f \over f-d_\mathrm{o}} = - \frac{f}{x_o} where f is the focal length, d_\mathrm{o} is the distance from the lens to the object, and x_0 = d_0 - f as the distance of the object with respect to the front focal point. A sign convention is used such that d_0 and d_i (the image distance from the lens) are positive for real object and image, respectively, and negative for virtual object and images, respectively. f of a converging lens is positive while for a diverging lens it is negative. For real images, M is negative and the image is inverted. For virtual images, M is positive and the image is upright. With d_\mathrm{i} being the distance from the lens to the image, h_\mathrm{i} the height of the image and h_\mathrm{o} the height of the object, the magnification can also be written as Therefore, in photography: Object height and distance are always and positive. When the focal length is positive the image's height, distance and magnification are and positive. Only if the focal length is negative, the image's height, distance and magnification are and negative. Therefore, the '''' formulae are traditionally presented as \begin{align} M &= {d_\mathrm{i} \over d_\mathrm{o}} = {h_\mathrm{i} \over h_\mathrm{o}} \\ &= {f \over d_\mathrm{o}-f} = {d_\mathrm{i}-f \over f} \end{align} Magnifying glass The maximum angular magnification (angle the object subtends on the retina at the near point versus the increased angle on the retina when the glass is within 25 cm of the eye) of a magnifying glass' thin converging lens, depends on how the glass and the object are held, relative to the eye. If the lens is held at a distance from the object such that its front focal point is on the object being viewed, the relaxed eye (focused to infinity) can view the image with angular magnification A different interpretation of the working of the latter case is that the magnifying glass changes the diopter of the eye (making it myopic) so that the object can be placed closer to the eye resulting in a larger angular magnification. Microscope The angular magnification of a microscope is given by M_\mathrm{A} = M_\mathrm{o} \times M_\mathrm{e} where M_\mathrm{o} is the magnification of the objective and M_\mathrm{e} the magnification of the eyepiece. The magnification of the objective depends on its focal length f_\mathrm{o} and on the distance d between objective back focal plane and the focal plane of the eyepiece (called the tube length) M_\mathrm{o}= - {d \over f_\mathrm{o}} The magnification of the eyepiece depends upon its focal length f_\mathrm{e} and is calculated by the same equation as that of a magnifying glass M_\mathrm{e}={25\ \mathrm{cm} \over f_\mathrm{e}} Telescope The angular magnification of an optical telescope is given by M_\mathrm{A}= - {f_\mathrm{o} \over f_\mathrm{e}} in which f_\mathrm{o} is the focal length of the objective lens in a refractor or of the primary mirror in a reflector, and f_\mathrm{e} is the focal length of the eyepiece. Measurement of telescope magnification Measuring the actual angular magnification of a telescope is difficult, but it is possible to use the reciprocal relationship between the linear magnification and the angular magnification, since the linear magnification is constant for all objects. The telescope is focused correctly for viewing objects at the distance for which the angular magnification is to be determined and then the object glass is used as an object the image of which is known as the exit pupil. The diameter of this may be measured using an instrument known as a Ramsden dynameter which consists of a Ramsden eyepiece with micrometer hairs in the back focal plane. This is mounted in front of the telescope eyepiece and used to evaluate the diameter of the exit pupil. This will be much smaller than the object glass diameter, which gives the linear magnification (actually a reduction), the angular magnification can be determined from M_\mathrm{A} = {1 \over M} = {D_{\mathrm{Objective}} \over {D_\mathrm{Ramsden}}}\,. ==Maximum usable magnification==

With any telescope, microscope or lens, a maximum magnification exists beyond which the image looks bigger but shows no more detail. It occurs when the finest detail the instrument can resolve is magnified to match the finest detail the eye can see. Magnification beyond this maximum is sometimes called "empty magnification". For a good quality telescope operating in good atmospheric conditions, the maximum usable magnification is limited by diffraction. In practice it is considered to be 2× the aperture in millimetres or 50× the aperture in inches; so, a diameter telescope has a maximum usable magnification of 120×. With an optical microscope having a high numerical aperture and using oil immersion, the best possible resolution is corresponding to a magnification of around 1200×. Without oil immersion, the maximum usable magnification is around 800×. For details, see limitations of optical microscopes. Small, cheap telescopes and microscopes are sometimes supplied with the eyepieces that give magnification far higher than is usable. The maximum relative to the minimum magnification of an optical system is known as zoom ratio. =="Magnification" of displayed images==

Magnification figures on pictures displayed in print or online can be misleading. Editors of journals and magazines routinely resize images to fit the page, making any magnification number provided in the figure legend incorrect. Images displayed on a computer screen change size based on the size of the screen. A scale bar (or micron bar) is a bar of stated length superimposed on a picture. When the picture is resized the bar will be resized in proportion. If a picture has a scale bar, the actual magnification can easily be calculated. Where the scale (magnification) of an image is important or relevant, including a scale bar is preferable to stating magnification. ==See also==