How Is Total Magnification Calculated

Conventional microscopes utilize multiple lenses, meaning it can be hard to discern the actual size of the image you are looking at. Moreover, microscopes utilize eye-pieces that block out all other light, meaning the person viewing has no real frame of reference for the size of the image displayed. This changes when viewing these images on a screen, as it is hard to tell how the size of the monitor affects the size of what you are seeing.

In this article, we break down the core components of an optical microscope to give you an understanding of how they work together. We also provide a mathematical formula for understanding the total magnification.

In addition, we explain ‘false magnification’ and how microscopes can advertise images that are lower quality than they would have you believe.

We will also go over how this measurement and the dimensions of your screen equipment can help you quantify the size of a microscopy image displayed on a monitor.

How Do I Calculate The Magnification of a Microscope?

A microscope is a complex device made of several intertwining mechanisms interacting with one another. It includes a platform for holding a specimen sample, levers for adjusting said platform, and a series of lenses providing the imaging. It’s important to understand there are two primary lenses used in microscopes.

The first is the objective lens, a highly magnified lens with between 40 and 100 times magnification that produces a high-resolution re-creation of the original image. These lenses are designed to be close to samples for clarity to minimize the refraction of light between the specimen and the lens.

One tactic used to help preserve this resolution is an oil immersion, the technique of actually connecting the sample and the lens with a highly refractive oil that helps the image cleanly pass through. On 100 times objective lenses, this is necessary to maintain clarity and depth of the visual information acquired.

The second is the optical lens, the lens the researcher looks into to see the image produced by the objective lens above the sample. This lens is less magnified than the objective lens and is designed to help amplify the image produced to a size visible by the human eye.

As Sciencing explains, if your sample were ten micrometers wide, and you amplified it with a 100 times objective lens, an image that is 1000 micrometers wide, or just one single millimeter, would be the result.

But, with a ten times optical lens, we can then examine that image at one centimeter in width, which is more manageable within the contained optics of a microscope’s housing.

In other words, the total magnification of a microscope is understood as the magnification of the objective lens multiplied by that of the optical lens. While optical lenses are typically a standard ten times, objective lenses tend to vary more and come in sizes of 4, 10, 40, or 100 times magnification.

With current technology, the maximum known magnification for light microscopes is 1000x, which is more than suitable for the most complex applications.

How Do I Calculate On-Screen Magnification?

When viewing a digitally captured microscopy image on a computer, it is hard to understand how big the subject you’re looking at is in real life. In other forms of microphotography, it is possible to put a scale behind the specimen for comparison, but this is an impossible solution at the microscopic level. Luckily, Microscope World shows us the steps and equations necessary.

Firstly, we must understand the magnification of our optical configuration, which differs slightly from the figures we saw above in a microscope. A microscope camera utilizes an optical lens smaller than the optical lenses used for human eyes, as a camera sensor can cleanly detect finer details than a person.

Your objective lens is unchanged, but you should document the magnification on your microscope’s c-mount adapter, which is where the camera connects to the device. The final calculation for this magnification is the same, so multiply the c-mount adapter by the objective lens.

For our example, our objective lens is x4, and our c-mount is 0.5x, so our total optical magnification is 2x.

Second, we need to understand the size of our monitor. An inch is 2.54 centimeters or 25.4 millimeters, and so we can simply multiply our monitor’s advertised diagonal length by 25.4 to understand the total millimeters from one corner to another.

Similarly, we need to understand the resolution of our sensor. Here’s a helpful chart to understand the diagonal millimeter length based on its overall chip size.

¼” Chip, 4MM Diagonal
1/3.2” Chip, 5.68 MM Diagonal
⅓” Chip, 6 MM Diagonal
1/2.5” Chip, 7.18 MM Diagonal
½” Chip, 8 MM Diagonal
1/1.8” Chip, 8.93 MM Diagonal
⅔” Chip, 11 MM Diagonal

With the millimeter lengths of both our monitor and the sensor used to capture the image, we can divide the monitor’s diagonal axis by the chip’s for our digital magnification.

As an example, a 19” monitor is 482.6 millimeters long diagonally, so if we used a ½” sensor to capture the image displayed, we could divide the monitor’s length by the sensor length (8, per the chart above) to understand our digital magnification as 60.325 times.

With this digital magnification, we simply need to multiply it by the optical magnification we discerned earlier. This means our formula would be 2 x 60.325, which is 120.65 times magnification on-screen, compared to the real-life sample we used to capture the photograph.

What is False Magnification?

Some lens makers may advertise microscopy solutions offering more than 1,000x, with figures up to 2,000x.

However, as Microscope Safari explains, these microscopes utilize larger optical lenses, which don’t generate any new detail but simply make the microscope image bigger. Instead, it is important to know your objective lens’s numerical aperture and multiply it by 1000, as this will provide the highest useful magnification to you.

For example, if a lens has a NA value of 0.65, and the highest magnification it achieves is 650x, then using a 20x eyepiece and a 40x objective would waste 150x of magnification on making the image bigger.

The point of microscopy is to uncover minute details in specimens and samples to properly evaluate them, such as counting certain proteins or study atoms. These lenses do accomplish their advertised goal, but not to provide greater clarity of your sample.

Instead, they provide inflated metrics that are appealing in advertisements but do not deliver enhanced results. When searching for your customized microscopy solution, be sure to evaluate the claims made by the manufacturer to ensure that they are realistic and are accomplished with the appropriate means and methods.

As outlined above, optical lenses hover around 10x, so you should avoid any size beyond that.

Conclusion

The magnification of the objective lens or microscope camera, multiplied by that of the optical lens, represents the total magnification.

The total magnification can be as low as 40 but reaches up to 1000, with exceptional magnification offered by certain solutions. On display, the millimeter diagonal length of your monitor is divided by the millimeter diagonal length of your camera’s imaging sensor to help understand the digital magnification.

When multiplied, these two numbers provide you with the precise answer for how magnified your microscopy image is. However, pay close attention to the optical lens magnification, as some manufacturers use larger lenses to inflate their magnification numbers.

This results in a microscope displaying bigger images but do not offer detail, and therefore are not of increased value.

Visit Navitar for more information on our Custom Microscope Objectives.

Sources:

Sciencing - How to Calculate Magnification on a Light Microscope | Sciencing.com

Microscope World - How to Calculate Microscope On-Screen Magnification | Microscopeworld.com

Microscope Safari - Basic Needs For The Microscope | microscopesafari.com