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## Microscope Magnification and Field of View Calculator

Microscope field of view diameter, *D*_{VF}

The calculator determines the microscope field of view from the known magnification of the objective lens and the field number of the eyepiece (ocular) lens. It can also be used to calculate the field of view for a higher power magnification if a lower power magnification field of view is known and to estimate the size of a specimen observed through the microscope.

**Example 1:** Calculate the field of view diameter of an optical microscope with a 45× objective lens, eyepiece field number 15 and without a tube lens (its magnification is 1×).

**Example 2:** Calculate the field of view diameter for a 45× objective lens if the field of view for an objective lens 5× is 3 mm.

**Example 3:** Estimate the size of a specimen for the field view determined in Example 2 if the number of objects, which fit across the field of view is 3.

### Microscope Field of View

**Input**

Eyepiece Lens Field Number (engraved on the eyepiece)

*FN*

Objective Lens Magnification

** M_{O}** ×

Tube lens magnification factor

** M_{T}** ×

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**Output**

Microscope Field of View Diameter

** D_{VF}** mm

### Microscope Field of View for Higher or Lower Objective Lens Magnification

Magnification of the lower power objective lens

** M_{LP}** ×

Lower power microscope field of view diameter

*D*_{LP}

Magnification of the higher power objective lens

** M_{HP}** ×

Microscope field of view diameter for a higher power objective lens

*D*_{HP}

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To calculate, enter the three values and click or tap the **Calculate** button. One other value will be calculated.

### Actual Size of a Specimen Calculator

**Input**

Microscope Field of View Diameter

*D*_{FV}

Number of Specimen in the Field of View

*N*

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**Output**

Estimated Specimen Size

** L_{sp}** mm

For a magnification of a digital microscope or a microscope with a camera, see our Digital Microscope Magnification Calculator. To calculate the magnification of an optical microscope, use our Microscope Magnification Calculator.

At the end of the calculator description, we will provide a review of a ** Miko India** microscope and tell you

**how NOT to buy a microscope**using this microscope as an example.

## Definitions and Formulas

Wide-field 10× eyepieces with field numbers 20 mm and 16 mm. The field number is not engraved on the left eyepiece; it was determined by means of measuring the internal diaphragm diameter. The eyeglasses sign on the left eyepiece shows that it is designed as a high point or eye relief eyepiece and can be used by people wearing eyeglasses.

### Calculation of the Microscope Field of View

The microscope field of view is the maximum diameter of the area visible when looking through the eyepiece (that will be the eyepiece field of view) or using a camera (that will be the camera field of view). The microscope field of view is limited by the objective lens, the diameter of the internal mechanical optical path (tube), the eyepieces used and the camera sensor size. If a full-frame DSLR camera is used for taking pictures and videos, its sensor size is usually larger than the other limiting factors.

Any microscope eyepiece is characterized at with least two numbers: its **magnification** (10× being the most common) and the field number. The **eyepiece field number** (abbreviated as FN and sometimes as FOV) is the diameter of the field view in millimeters measured at the intermediate real image plane. The field of view is defined by a fixed (because it cannot be changed) circular opening (diaphragm) of the eyepiece, which, depending on its design, can be either between the eyepiece lenses or below them. In most cases, the field diaphragm opening diameter (called field number of FN) of the eyepiece determines the view field diameter.

Fixed internal diaphragms of FN=16 mm and FN=20 mm eyepieces. 1. Eyepiece diaphragm

The **microscope field of view diameter** in the plane where the specimen is placed is defined by the following formula:

where

*D _{FV}* is the diameter of the view field in the specimen plane,

*FN* is the field number in millimeters (it refers to the diameter in millimeters of the fixed diaphragm inside the eyepiece; it is usually marked on the eyepiece and sometimes called Field of View number),

*M*_{O} is the objective magnification (marked on the objective lens), and

*M*_{T} is the tube lens magnification factor (if any; the tube lens is placed in the microscope optical path between the objective and the eyepiece to produce an intermediate real image).

From this formula, we can determine the field number:

For example, for the 10× lens, tube magnification factor 1×, and FN = 15, we have

1 mm (1 division = 0.01 mm) and 50 mm (1 division = 0.5 mm) calibration slides

As you can see from the above formula, the ocular magnification does not have any effect on the field of view. For example, 10×/18 and 12×/18 eyepieces have the same eyepiece field of view diameter FN = 18 mm.

Note that this calculation is only an estimate. To get the actual field of view of your particular microscope with a particular objective and eyepiece lenses, your microscope needs to be calibrated using a calibration slide. This calibration must be performed for every eyepiece and objective lens combination.

If an eyepiece is substituted with a camera, especially if the camera is installed instead of the binocular head, then the field of view will be determined by the size of the camera image sensor (for cameras with relatively small sensors) and/or the microscope objective. When using a camera with a small sensor, it is common to use a reduction lens, which is installed on the camera. A camera with a large sensor, on the other hand, will see the whole field determined only by the microscope objective.

An aphis viewed through the same 10× plan achromat lens and different 10× eyepieces with FN = 16.7 and FN = 20; note the same size of the aphis image and different field sizes due to different eyepieces

As was mentioned above, the field diameter usually depends on the magnification of the microscope objective and the field diaphragm of the eyepiece. However, the design of the objective lens also imposes a limit on the field of view. In early microscopes, objective lenses provided the maximum diameter of the field view measured at the intermediate real image plane less than 18 mm. Modern objectives, not only expensive plan apochromats, but even commonly used plan achromats provide the maximum usable diameter measured at the intermediate plane that can exceed 28 mm. For example, the no-name plan achromats pictured below provide max. diameter of the field of view at intermediate image plane 19.2–39.0 mm depending on the objective magnification:

Magnification of the Objective Lens | Aperture | Microscope Field of View | Diameter of the Intermediate Image Plane (on the camera image sensor) |
---|---|---|---|

100× | 1,25 | 0,39 mm | 39,00 mm |

40× | 0,65 | 0,98 mm | 39,20 mm |

10× | 0,25 | 3,60 mm | 36,00 mm |

4× | 0,10 | 4,80 mm | 19,20 mm |

At the same time, the field of view when viewed through oculars is limited by the ocular field of view. The following table shows the field of view for a 10 × 20 mm eyepiece with plan achromatic objectives:

Magnification of the Objective Lens | Aperture | Microscope Field of View |
---|---|---|

100× | 1,25 | 0,18 mm |

40× | 0,65 | 0,46 mm |

10× | 0,25 | 1,90 mm |

4× | 0,10 | 4,50 mm |

Note that to shoot the pictures of Ascaris lumbricoides eggs and chicken blood cells shown below we used the same no-name objective lenses pictured below and a Canon 5D Mk II DSLR full-frame camera.

### Calculation of the Microscope Field of View for Higher or Lower Objective Lens Magnification

Four no-name plan achromat objective lenses ($162)

Sometimes the microscope field of view is known for a particular combination of an ocular and an objective lens and we need to determine the field of view for an objective lens with higher or lower magnification. The following formula is used to calculate the microscope field of view for a higher power magnification if a lower power magnification field of view is known.

where

D_{HP} is the microscope field of view diameter for a higher power objective lens,

D_{LP} is the microscope field of view diameter for a lower power objective lens,

M_{HP} is the higher power objective lens magnification, and

M_{LP} is the lower power objective lens magnification.

For example, for a microscope with a 10× eyepiece and 45× objective, the magnification is 10 × 45 = 450 and the field of view is 0.33 mm. What will be the field of view if we change the objective lens to 100×? To calculate, we will use the formula above.

Solving this proportion for D_{HP}, we will have

A microscope with a 40× objective and a 10×/20 ocular; the field of view is 450 μm; the size of a fertile egg (top right) of Ascaris lumbricoides is 60 μm

### Calculation of the Actual Size of a Specimen

To estimate the actual size of a specimen, place it on the stage, select objective lens with the most appropriate magnification and estimate the number of objects *N* that can fit across the field of view circle *D*_{FV}. The actual size *L*_{sp} will be determined using the following formula:

A microscope with a 40× objective and a 10×/20 ocular; the field of view is 450 μm; the size of a chicken blood cell is 12 μm;

For example, approximately 2.5 microorganisms may fit across the diameter of the field of view, which equals 0.33 mm. Then the estimated size of the microorganism is

### How NOT to Buy a Microscope (Using a Miko India Biological Microscope as an Example)

This is how this Miko microscope looks like if you do not disassemble it to view what’s inside

Below you will find a very unusual description of the microscope used for making illustrations for this and other calculators. However, it is hard to resist the temptation of telling a story about how I bought a new microscope made by Miko India, a little-known microscope manufacturer who positions itself on the very competitive microscope market as “one of the leading manufacturers and exporters of scientific/laboratory instruments” I wanted to give it a try because sometimes startups can make very good products. Besides, an impressive track record for the Indian Space Research Organization shows that they can make really good optical instruments. Here’s what I got.

I wanted to buy a microscope for a long time because I often need to take pictures of small things like microchips for these unit converters and calculators. This time, I decided to kill two birds with one stone — to acquire a microscope and to make several microscope calculators using my new microscope to make experiments and illustrations. I am not an expert in optics and when it is necessary to study something new, I always try to learn theory through experiments and practical activities.

So, here we are with a brand-new binocular microscope purchased on eBay for US $163 from **Miko India**, “one of the leading manufacturers and exporters of scientific/laboratory instruments, microscopes, etc.” Remembering that a picture is worth a thousand words, I am going to present some pictures showing what’s inside of this “precision optical instrument” that looks nice from the outside.

I should note that strangely enough, this microscope has a good quality stand, mechanical stage, and revolving nose piece. All mechanical parts are working smoothly. However, everything else is of very poor quality and covered with dirt and chipped paint. Note that **Miko India** positions this microscope as a precision biological instrument and not a toy or a student microscope.

All objective lenses are scratched and dirty. I did not disassemble them; however, I am sure the quality of the optical surfaces is not better than the quality of metal and plastic parts of these lenses.

More pictures of lenses reveal that they are poorly machined and have poor chrome coating. A lot of scratches and chipped parts.

- Now let us look at what’s inside the electrical box. All metal parts were made by an amateur in his or her garage and definitely not at the optical factory of “one of the leading manufacturers and exporters of scientific/laboratory instruments”.
- The dust and dirt shown in this picture were everywhere in the microscope. I had to clean it before testing.

1. Wrong ground connection; the ground wire is connected to the plastic casing. 2. Poorly made LED bracket with inadequate surface area for LED cooling. 3. No thermal grease was placed between the LED heatsink and the bracket

This optical path above the revolving nosepiece is supposed to be nicely machined and covered in black paint to reduce internal reflections; in this device, the paint is white and there are several pockets in the aluminum body

Rudely made prisms with rusty brackets and bent screws in the microscope head.

Scratched optical surfaces of the Abbe condenser.

After a day or so of repair work and replacement objectives and eyepieces with good quality optics, I now have a good microscope.

In my opinion, the microscope price is definitely not an indicator of quality. When you pay for a brand name microscope, you pay 90% or even more for its name (you can as well pay for the air) and 10% for the thing itself. If you understand and can easily learn how things work, you can buy no-name things. If, however, you do not like to turn on your brains, it is better to pay for a brand name. I am sure that for about $200 and even $150 one can buy a decent quality binocular biological microscope made in China. Anyway, almost everything is made in China nowadays! However, sometimes you can get a thing as I described here.

Still, after spending some time and money, I used this microscope to prepare illustrations for all microscope calculators that you can find on this web site, including this calculator. I am going to use this microscope for a long time.

Dit artikel is geschreven door Anatoly Zolotkov

### Misschien ben je ook geïnteresseerd in rekenmachines in de categorie Microscopie:

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Microscope Magnification Calculator

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Microscope Objective Focal Length Calculator

Rekentools Microscopie

## FAQs

### How do you calculate field of view and magnification? ›

**Field of View = Field Number (FN) ÷ Objective Magnification**

Higher power lenses will allow you to view tiny objects, so the angle of view will be small; low power lenses will do the opposite and let you view bigger (wider) objects. Learn more about microscope magnification here.

**What is 10x 40x magnification? ›**

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**.

**How do you calculate the magnification of a microscope? ›**

To figure the total magnification of an image that you are viewing through the microscope is really quite simple. To get the total magnification **take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X**.

**What is the field of view at 40x in micrometers μm? ›**

...

Objective | Diameter Of Field Of View | Magnification (10x Ocular) |
---|---|---|

40x | 0.4 mm (0.45) | 400x |

100x | 0.2 mm (0.178) | 1000x |

**What is the formula for FOV? ›**

You can calculate the FOV using the formula: **2 x the tangent of ½ the angle x distance**. You can measure (and “map out”) the practical FOV with a quick field test to check your math!

**How FOV is calculated? ›**

The formula that it implements is **FOV = 2 arctan (x / (2 f))**, where x is the diagonal of the film. The FOV is measured across the frame's diagonal, and is therefore smaller across the horizonal dimension, and even smaller across the vertical dimension.

**What is the total magnification at 4x 10x and 40x? ›**

Grades 1-8 typically will buy a monocular compound microscope with 3 objective lenses: 4x, 10x, 40x for maximum total magnification of **400x**.

**Is 40x the same as 400x? ›**

High Power Objective Lens (40x)

**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.

**What magnification is 100x? ›**

At 100x magnification **you will be able to see 2mm**. At 400x magnification you will be able to see 0.45mm, or 450 microns. At 1000x magnification you will be able to see 0.180mm, or 180 microns.

**What is the formula to calculate magnification? ›**

**Magnification = image size / actual size**. Actual size = image size / magnification. Image size = magnification x actual size.

### What is magnification formula? ›

Calculating magnification with the help of the lens formula:

The magnification of a lens is defined as the ratio of the height of an image to the height of an object. It is also given in terms of image distance and object distance. It is equal to the ratio of image distance to that of object distance. **m = h ′ h = v u**.

**What is 400x magnification in mm? ›**

At 400x magnification you will be able to see 0.45mm, or 450 microns. At 1000x magnification you will be able to see 0.180mm, or 180 microns.

**What is the field of view for 10x? ›**

For example, an eyepiece having a magnification of 10x typically has a field number ranging between **16 and 18 millimeters**, while a lower magnification eyepiece (5x) has a field number of about 20 millimeters.

**How many mm is 4x magnification? ›**

Objective Lenses | Eyepiece Lenses | |
---|---|---|

4x | 20x | 5mm |

10x | 1.8mm 1800um | |

40x | 0.45mm 450um | |

100x | 0.18mm 180um |

**What is the FOV of the 40X objective? ›**

Answer and Explanation: Now, the FOV at 40X magnification is 6000μm, and the magnification has been increased to 400X (10 times more), therefore Field of vision will decrease accordingly.

**What angle of view is 24mm? ›**

24mm (16mm) encompasses an angle of view of **84 degrees**, which is relatively wide. This focal length can help to retain a sense of space when photographing expansive landscapes.

**How do you convert focal length to FOV? ›**

Focal length (f) and field of view (FOV) of a lens are inversely proportional. For a standard rectilinear lens, **FOV = 2 arctan x/2f**, where x is the diagonal of the film.

**What is the unit of FOV? ›**

In astronomy, the field of view is usually expressed as an angular area viewed by the instrument, in **square degrees**, or for higher magnification instruments, in square arc-minutes.

**What FOV is normal? ›**

The human eye and field of view

Each individual eye has a **horizontal FOV of about 135 degrees and a vertical FOV of just over 180 degrees**. Stitching together the monocular FOV yields a binocular FOV of around 114 degrees of view horizontally. This FOV is necessary for depth perception.

**What is FOV value? ›**

Own Risk: Transit insurance is taken by the Shipper to protect against any loss, damage or pilferage during transit of the shipment. Our responsibility is limited to issuing a Certificate of Facts in the event of loss.

### What is the total magnification of 10X and 100X? ›

Answer and Explanation: The total magnification is **the magnification of the ocular lens (10) multiplied by the objective lens (100)**. If we multiply 100 x 10 = 1,000. This is noted as the total magnification is 1000x, or 1000 times the size of the specimen.

**What is the total magnification of 10X 10X? ›**

The total magnification is the product of the magnifications of two lens systems. Hence, the microscope which has a 10X objective lens and 10X ocular lens, it would magnify the object by 10 × 10 = **100 times**. Was this answer helpful?

**What is the total magnification if you use the 10X objective 40x 100X? ›**

Objective lens X Ocular lens = | Total magnification | |
---|---|---|

For example: | low power: | (10X)(10X) = 100X |

high dry: | (40X)(10X) = 400X | |

oil immersion: | (100X)(10X) = 1000X |

**What can you see with 2000X magnification? ›**

With a limit of around 2000X magnification you can view **bacteria, algae, protozoa and a variety of human/animal cells**. Viruses, molecules and atoms are beyond the capabilities of today's compound microscopes and can be viewed only with an electron microscope.

**What is bigger 10x or 40x? ›**

It's easy to understand. **A 40x objective makes things appear 40 times larger than they actually are**. Comparing objective magnification is relative—a 40x objective makes things twice as big as a 20x objective while a 60x objective makes them six times larger than a 10x objective.

**Is a 400x microscope good? ›**

– Is standard 400x magnification okay, or do you need 1000x magnification to see greater cell detail? **400x is ideal for high school biology**; 1000x is best for college microbiology.

**What is the total magnification of 10x and 50x? ›**

Therefore, we multiply the ocular objective lens magnification (10x) with the high power objective lens (50x); hence, the total magnification equals **500x**.

**What are the 4 types of magnification? ›**

There are four ways of creating magnification: Increase the size of the object Decrease the viewing distance Transverse magnification Telescopic magnification.

**Is there 1000x magnification? ›**

1000x is about as microscopic as microscopy can get. **Magnification levels include 40x, 100x, 400x and 1,000x**. At 1000x magnification, you can observe samples and specimens as small as 0.180mm, or 180 microns, across.

**What is total magnification and how is it calculated? ›**

Total magnification of an object observed through the eyepieces (ocular lens) is calculated by **multiplying the ocular lens magnification times the magnification of the objective lens being used** (either: 4X, 10X, 20X, 40X, 100X, etc.). “X” is placed after obtaining the total magnification number.

### What is the magnification of 1? ›

A magnification of 1 (plus or minus) means that **the image is the same size as the object**. If m has a magnitude greater than 1 the image is larger than the object, and an m with a magnitude less than 1 means the image is smaller than the object.

**What is the magnification of 10x? ›**

A hand-lens, for example, might be labeled with 10x, meaning the lens magnifies the object to look ten times larger than the actual size. Compound microscopes use two or more lenses to magnify the specimen.

**What does 200x magnification mean? ›**

When people talk about “Magnification” 400x or 200x, they often really mean **the size of the fiber area compared to the entire viewing zone**. Under 400x, the fiber area occupies a greater portion of the viewing zone than that under 200x.

**What is the resolution of a 40x microscope? ›**

THE RESOLUTION OF A 40x plan achromatic objective, which has a typical numerical aperture of 0.65, is **0.42 micrometers**.

**What does 7x magnification mean? ›**

The first number given is the power or magnification. A 7x (**seven power**) binocular will make an object look seven times closer or seven times larger than you would see with the unaided eye.

**What is the total magnification of 40? ›**

40 x 10 = 400, so the total magnification of this microscope would be **400 times** using the 40x lens.

**What does a magnification of 0.5 mean? ›**

The negative sign of magnification indicates that the image is real while 0.5 indicates that **the image is diminished**.

**What magnification is 800mm? ›**

Technical data | |
---|---|

Focal length | 800 mm |

Aperture (max/min) | f/5.6 – f/32 |

Close focus distance | 19.7 ft / 6.0 m |

Max. magnification | 0.14× |

**What is the magnification of 600mm? ›**

Variable focal length lenses with a maximum focal length of between 400mm and 600mm are by far the most popular lenses for bird photography as they provide 8X magnification at 400mm and **12X magnification** at 600mm when shooting with a full-frame sensor camera.

**What magnification is 300mm? ›**

Here is an example: For a 300mm lens, divide 300 by 50 to get **6x magnification**.

### What is the field of view at 20x? ›

A 20x objective with a field number of 18 would actually have a FOV of **0.9 mm**. Likewise, a 100x objective with a field number of 18 would have a FOV of 0.18 mm. The more an object is magnified, the smaller the field of view will be.

**What is the field of view diameter at 40x total magnification? ›**

At 40x total magnification, the diameter of the field of the view dFOV is 8.7 millimeters, what...

**What is a 90 degree field of view? ›**

At 90 degree FOV, you will get **2 feet for every 1 foot of distance from the camera**. In this case, 10 feet will provide 20 feet of width. What you will notice is the majority of professional/business grade video conferencing are within this (and the previous) category.

**What magnification is 6 24x50? ›**

Magnification | 6 – 24 x |
---|---|

Effective lens diameter | 44.9 – 50.0 mm |

Light transmission | 90% |

Exit pupil diameter | 7.5 – 2.1 mm |

Twilight factor | 16.4 – 34.6 |

**What can you see at 400x magnification? ›**

400x: This magnification is useful for looking inside cells. If you have prepared slides of cell divisions, then you are able to see the individual chromosomes quite well. The depth of field is now small and you have to operate the fine focus knob continuously. The shape of bacteria is now clearly visible.

**How far is 6x magnification? ›**

At 6x magnification, you should be able to shoot out to **1000 yards**, although not extremely accurately. The sweet spot is closer to 400 yards for optimum clarity and accuracy. This is great for 3 gun competitions and most hunting situations.

**What is the FOV at 400X total magnification? ›**

Field of view is how much of your specimen or object you will be able to see through the microscope. At 40x magnification you will be able to see 5mm. At 100x magnification you will be able to see 2mm. At 400x magnification you will be able to see 0.45mm, or 450 microns.

**How do you calculate the field of a microscope? ›**

The field size or diameter at a given magnification is calculated as **the field number divided by the objective magnification**. If the ×40 objective is used, the diameter of the field of view becomes 20 mm/40 (compared with no objective) or 0.5 mm.

**What are the 3 types of magnification? ›**

The compound microscope typically has three or four magnifications - **40x, 100x, 400x, and sometimes 1000x**. At 40x magnification you will be able to see 5mm. At 100x magnification you will be able to see 2mm. At 400x magnification you will be able to see 0.45mm, or 450 microns.

**What is the magnification of 40? ›**

**A 40x objective makes things appear 40 times larger than they actually are**. Comparing objective magnification is relative—a 40x objective makes things twice as big as a 20x objective while a 60x objective makes them six times larger than a 10x objective.

### What is the field of view for 10X? ›

For example, an eyepiece having a magnification of 10x typically has a field number ranging between **16 and 18 millimeters**, while a lower magnification eyepiece (5x) has a field number of about 20 millimeters.

**What can you see at 2000X magnification? ›**

With a limit of around 2000X magnification you can view **bacteria, algae, protozoa and a variety of human/animal cells**. Viruses, molecules and atoms are beyond the capabilities of today's compound microscopes and can be viewed only with an electron microscope.

**What magnification is 4x? ›**

Simply put, the “4” is the magnification power of the scope. If the magnification is 4x, it means your target will be magnified **4 times larger than what the naked eye sees**. The singular “4” also indicates that this scope has a fixed magnification. This means that you can't zoom in and out with this scope.

**What is a field calculator? ›**

The ^{Field} ^{Calculator}. button in the attribute table **allows you to perform calculations on the basis of existing attribute values or defined functions**, for instance, to calculate length or area of geometry features.

**What is the field of view of a 20x objective? ›**

A 20x objective with a field number of 18 would actually have a FOV of **0.9 mm**. Likewise, a 100x objective with a field number of 18 would have a FOV of 0.18 mm. The more an object is magnified, the smaller the field of view will be.

**What can you see at 100x magnification? ›**

Field of view at 100x magnification is approximately 2mm. Field of view at 400x magnification is approximately 0.45mm, or 450 microns. Field of view at 1000x magnification is approximately 0.180mm, or 180 microns.