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# How to Calculate a Maximum Useful Magnification

Updated July 19, 2017

The maximum useful magnification estimates the power of an optical instrument, such as a telescope or microscope, to magnify an object with useful detail. Magnifying an image beyond the maximum useful magnification is referred to as empty magnification, where the image is magnified but no greater detail is seen and the quality of the image deteriorates. The maximum useful magnification does not include factors outside the instrument such as atmospheric conditions for telescopes and specimen quality for microscopes.

Identify the objective lens (for refracting telescopes) or mirror (for reflecting telescopes) on the telescope. The objective is the light-gathering lens or mirror in the optical system. In reflecting telescopes, the objective mirror is located in the rear of the telescope tube. In refracting telescopes, the objective lens at the top of the telescope tube.

Find the diameter of the objective lens or mirror in inches. The diameter of the objective is usually provided in either inches or millimetres.

Multiply the objective diameter by 50. The product is the maximum useful magnification. For many telescopes, the maximum useful magnification is estimated at 50 times the objective diameter in inches. For example, a telescope with a 2.4-inch diameter objective would have a maximum useful magnification of 120x (2.4 x 50 = 120). Alternatively, you can multiply the objective diameter in millimetres by two to determine the maximum useful magnification. Using this equation, a 60mm diameter objective would have a maximum useful magnification of 120x (60 x 2 = 120). Note that these equations are estimates with some telescopes giving a maximum useful magnification as high as 100 times per inch or as low as 20 times per inch of objective diameter.

Select the objective lens for determining the maximum useful magnification. The objective lenses are located on the nosepiece above the stage. Maximum useful magnification will vary according to the objective lens you are using.

Identify the numerical aperture of the objective. You can usually find this engraved on the side of the objective lenses. The numerical aperture measures the ability of the microscope to gather light and resolve detail at a fixed distance from the lens. The numerical aperture depends on the medium the light passes through. Oil produces a higher numerical aperture than air and is why high-power objective lenses are known as oil immersion lenses.

Multiply the numerical aperture of the objective by 1,000 to produce the maximum useful magnification. For example, a numerical aperture of 0.95 would produce a maximum useful magnification of 950x (0.95 x 1,000 = 950). Note that microscope objectives also have a minimum useful magnification estimated by multiplying the numerical aperture by 500. The minimum useful magnification of an objective with a numerical aperture of 0.95 would be 475x (0.95 x 500 = 475).

#### Things You'll Need

• Telescope objective diameter
• Microscope objective diameter