Magnification

Magnification is the process of increasing the apparent size of an object. It is important to note that magnification does not change the physical size of the object itself. Instead, it changes how large the object appears to an observer. This change is measured using a size ratio called optical magnification. This value is a dimensionless number, meaning it has no units like inches or centimeters. When the ratio is greater than one, the object looks larger. If the ratio is less than one, the process is called de-magnification, which makes the object appear smaller.

To understand how magnification works, we must look at different types of measurement. For real images, such as those projected onto a screen, we use linear magnification. This measures the change in a linear dimension, like millimeters. However, many optical instruments use an eyepiece. For these tools, we use angular magnification. This refers to the angle the object covers at the focal point. For example, the Moon has an average angular size of about 0.52 degrees from Earth. If you view it through 10x binoculars, it appears to cover an angle of about 5.2 degrees.

Different instruments use specific mechanisms to achieve magnification. A magnifying glass uses a positive, or convex, lens. This lens allows a user to hold an object closer to the eye to see it better. A microscope works much like a telescope. It uses an objective lens to create a large image of a small object. This allows the viewer to see details from a comfortable distance. A telescope uses a large objective lens or a primary mirror. It creates an image of a distant object, which is then examined through a smaller eyepiece lens.

In physics, the math behind a single thin lens involves several variables. The linear magnification of a thin lens depends on the focal length and the distances of the object and the image. We use a sign convention to keep track of these values. For a converging lens, the value is positive. For a diverging lens, the value is negative. If the magnification is negative, it means the resulting image is inverted, or upside down. There is also longitudinal magnification, which measures magnification along the optical axis. This value is always negative, meaning the object and image move in the same direction.

Photography relies on creating real images, which are usually inverted. In photography, a different sign convention is often used. In this system, object height and distance are always treated as positive. If the lens has a positive focal length, the image height and distance are also positive. This differs from the standard Cartesian sign convention used in general physics. This distinction is important for scientists and photographers when calculating how light will behave through a camera lens.

Every optical instrument has a limit to its usefulness. This limit is reached when an image is made larger but shows no additional detail. This phenomenon is called "empty magnification." For a telescope, the maximum usable magnification is limited by diffraction. A common rule is that the maximum magnification is 2 times the aperture in millimeters. For a telescope with a 50 millimeter diameter, the maximum usable magnification is 120x. Microscopes also have limits based on their setup. A standard optical microscope reaches about 800x magnification. If a scientist uses oil immersion, they can reach a resolution of about 1200x.

Finally, we must be careful when looking at magnification in print or on digital screens. Editors often resize images to fit a magazine page, which makes written magnification numbers incorrect. Digital images also change size depending on the computer screen being used. To solve this, scientists use a scale bar, also called a micron bar. This is a line of a known length placed on the image. If the image is resized, the scale bar resizes along with it. This allows anyone to calculate the true size of the object regardless of the display size.