magnification - Magnification as a number (optical magnification), Other uses

A measure of an optical system's power to reduce or enlarge an image. For a simple lens, magnification equals the ratio of the angle subtended at the eye with the lens to the angle subtended at the eye without the lens. It is approximately equal to the ratio of size of image to size of object.

For the 2001 album of progressive rock band Yes, see Magnification (album).

Magnification is the process of enlarging something only in appearance, not in physical size. In all cases, the magnification of the image does not change the perspective of the image.

Magnification as a number (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.

Linear or transverse magnification — For real images, e.g., images projected on a screen, size means a linear dimension (measured, e.g., in millimeters or inches). Angular magnification — For optical instruments with an eyepiece, the linear dimension of the image seen in the eyepiece (virtual image in infinite distance) cannot be given, thus size means the angle subtended by the object at the focal point (angular size). Thus, angular magnification is defined as , where is the angle subtended by the object at the front focal point of the objective and is the angle subtended by the image at the rear focal point of the eyepiece. 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 of 25 cm from the eye.

Calculating the magnification of optical systems

Single lens: The linear magnification of a thin lens is where f is the focal length and S is the distance from the lens to the object. Telescope: The linear magnification is given by where fo is the focal length of the objective lens and fe is the focal length of the eyepiece. The angular magnification is given by Magnifying glass: The angular magnification of a magnifying glass depends on how the glass and the object are held, relative to the eye. If the lens is held such that its front focal point is on the object being viewed, the relaxed eye can view the image with angular magnification If instead the lens is held very close to the eye, and the object is placed close to the lens, a larger angular magnification can be obtained, approaching Here, f is the focal length of the lens in centimeters. Microscope: The angular magnification is given by where Mo is the magnification of the objective and Me the magnification of the eyepiece. The magnification of the objective depends on its focal length fo and on the distance d between objective back focal plane and the focal plane of the eyepiece (called the tube length): .

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 focussed 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 Ramsden disc. 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

MA = 1 / M = DObjective / DRamsden

Other uses

One can also magnify sounds (see amplification).