What is the total magnification of the microscope using a 4x a 10X and a 40x objective?

The quality of a microscope is based on its ability to perform two specific tasks: 1) magnify, and 2) resolve detail.

Magnification is the ability to produce enlarged images of objects.

Source: Davidson and Abramowitz

In the compound microscope, magnification is performed by two lens systems, the objective lens and the eyepiece.  As discussed earlier, The objective lens forms the primary magnified image of the specimen.   This primary image is a magnified inverted, real image that comes to focus at a fixed distance, about 160 mm, inside the microscope tube, i.e., near the top of the microscope tube just below the eyepiece.  The eyepeice, which contains the ocular lenses, magnifies this primary image.  The eye sees this secondary image as a virtual image about 10 inches from the eye.

The total magnifying power of the microscope is the product of the magnifying power of these two lens systems. When using a standard 10X eyepiece in combination with the four most-commonly used objectives (4X, 10X, 40X and 100X), the total magnifying power of a typical compound bright-field microscope has a range of 40X to 1000X (see table below).

Resolution, or resolving power, is the ability to distinguish two separate points as being separate and distinct.

The resolving power of a microscope determines the degree of detail that is visible. Resolution is expressed as the minimum distance that can be resolved. Under normal viewing conditions, the resolving power of the human eye is approximately 200 micrometers. Objects separated by less than this distance appear as one object to the unaided eye. The resolution of a typical compound microscope is approximately 0.2 micrometers, 3 orders of magnitude better than the human eye.

 While resolution equations vary slightly among applications, microscope resolution is generally calculated using the following equation formulated by Abbe.

d = lambda / N.A.objective + N.A.condenser

where d is the minmum resolution distance (MRD), lambda is the wavelength of illuminating light in use, and N.A. is the numerical aperture of the objective and condenser lenses in use. The equation shows that microscope resolution depends directly on the wavelength of light used to illuminate the specimen and inversely on the numerical aperture of the objective and condenser lenses.

Based on the Abbe equation, resolution is improved when shorter wavelengths of light are used to illuminate the specimen. White light, which is composed of a mixture of wavelengths from approximately 350 nm to 700 nm (average about 525 nm), is used for routine histological examination. Pure violet light, which has a wavelength of 350 nm, can be used to improve resolution, but its use can be impractical when examining stained histological specimen.

The Abbe equation also indicates that resolution is maximized when objective and condeneser lenses with the greatest possible numerical apertures are used. The numerical aperture (N.A.) of a lens is an index of the angle of the cone of light that can be produced by or collected by a lens. Lenses with high numerical apertures can collect light cones of greater angle, increasing the resolution.

Ideally, the N.A. of the condenser lens should match that of the obejctive lens in use. As described under Light Path, the user can bring the N.A. of the condenser close to that of the objective by adjusting the condenser's aperture diaphragm. 

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A microscope's total magnification is a combination of the eyepieces and the objective lens. For example, a biological microscope with 10x eyepieces and a 40x objective has 400x magnification. There are however, a few limits to the amount of total magnification that can be reached before empty magnification comes into play. Empty magnification occurs when the image continues to be enlarged, but no additional detail is resolved. This is often the case when higher magnification eyepieces are used. In order to avoid empty magnification, there are a few simple steps that are helpful to follow.

Eyepiece and Objective Combinations for Optimal Magnification

When selecting a combination of eyepieces and objective lenses for the optimal magnification, without ending up with "empty magnification" it is important to consider the numerical aperature (NA) of the objective. The numerical aperture of a microscope objective defines the objective's resolution. Each microscope objective has a minimum and maximum magnification necessary for the details in an image to be resolved. A simple formula for the minimum value is (500 x NA). And for the maximum magnification (1000 x NA). Magnifications higher than this value will result in empty magnification, or an image that has a poor resolution. The table below shows some typical NA values with their corresponding objective and provides a range of useful magnification combinations. The blank boxes in the table would provide empty magnification and should be avoided. For example, pairing 20x eyepieces with a 100x objective would not provide good resolution and would result in empty magnification. To determine this, we took 1.25NA x 1000 = 1250 magnification maximum. However, the combination of the 100x objective x 20x eyepieces = 2000, which is above the maximum magnification.

Range of Useful Magnification based on NA of Objectives

If you have any questions about your microscope's magnification, contact Microscope World.

This entry was posted on March 16, 2020 by Accu-Scope.

Most compound microscopes come with interchangeable lenses known as objective lenses. Objective lenses come in various magnification powers, with the most common being 4x, 10x, 40x, and 100x, also known as scanning, low power, high power, and (typically) oil immersion objectives, respectively. Let’s take a closer look at each of the different magnifications of objective lenses and when you would use them.

Scanning Objective Lens (4x)

A scanning objective lens provides the lowest magnification power of all objective lenses. 4x is a common magnification for scanning objectives and, when combined with the magnification power of a 10x eyepiece lens, a 4x scanning objective lens gives a total magnification of 40x. The name “scanning” objective lens comes from the fact that they provide observers with about enough magnification for a good overview of the slide, essentially a “scan” of the slide. Some objectives with even lower power are discussed in Specialty Objectives below.

Low Power Objective (10x)

The low power objective lens has more magnification power than the scanning objective lens, and it is one of the most helpful lenses when it comes to observing and analyzing glass slide samples. The total magnification of a low power objective lens combined with a 10x eyepiece lens is 100x magnification, giving you a closer view of the slide than a scanning objective lens without getting too close for general viewing purposes.

High Power Objective Lens (40x)

The high-powered objective lens (also called “high dry” lens) is ideal for observing fine details within a specimen sample. The total magnification of a high-power objective lens combined with a 10x eyepiece is equal to 400x magnification, giving you a very detailed picture of the specimen in your slide.

Oil Immersion Objective Lens (100x)

The oil immersion objective lens provides the most powerful magnification, with a whopping magnification total of 1000x when combined with a 10x eyepiece. But the refractive index of air and your glass slide are slightly different, so a special immersion oil must be used to help bridge the gap. Without adding a drop of immersion oil, the oil immersion objective lens will not function correctly, the specimen will appear blurry, and you will not achieve an ideal magnification or resolution. Oil immersion lenses are also available from some manufacturers in lower magnifications, and provide higher resolution than their "high dry" counterparts.

Specialty Objective Lenses (2x, 50x Oil, 60x and 100x Dry)

There are several other objective lens magnifications available with utility for particular applications. The 2x objective, widely used in pathology, has only ½ the magnification of a 4x scanning lens, thus providing a better overview of the sample on the slide. The 50x oil immersion objective, often used in place of the 40x objective, is used as a gold standard for observing blood smears. The 60x objective, often available in either dry or oil immersion, provides 50% greater magnification than a 40x lens. The 60x dry is sometimes chosen over a 100x oil immersion lens for higher magnification without the need to use immersion oil.  Finally the 100x dry objective doesn’t need immersion oil to deliver high magnification (still 1000x when combined with 10x eyepieces). However, the numerical aperture (an indication of resolving power of an objective) of a 100x dry objective is much lower than that of a 100x oil immersion objective and, as a result, the ability of the lens to resolve fine details in the specimen is much lower, too.

It is important to always use the correct immersion media (e.g. air, water, oil, etc.) that is specified by your objective lens.

• The image produced by the wrong immersion media will be blurry. In general, objectives are engineered to "look" through an immersion medium with a particular refractive index (a topic for another article). For example, air has a refractive index of close to 1.0, whereas standard immersion oil has a refractive index of ~1.51.
• You can damage the objective if you use the wrong immersion oil.

If you are interested in buying various types of objective lenses for your microscope in the classroom, laboratory, research facility, or any other purpose, ACCU-SCOPE can provide the products you are looking for. Contact us today to learn more about our objective lenses and other microscope accessories.