Magnification - Magnification As A Number (optical Magnification)

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, 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 in 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:

,

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.

• Example: The angular size of the full moon is 0.5°. In binoculars with 10x magnification it appears to subtend an angle of 5°.

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: 25 cm from the eye.

Optical magnification is sometimes referred to as "power" (for example "10× power"), although this can lead to confusion with optical power.