# How to Calculate Total Magnification

## What is Total Magnification

Total magnification refers to the level of enlargement or amplification achieved when viewing an object through an optical instrument, such as a microscope or a telescope. It is a very important parameter that quantifies how much larger an object appears when observed through the optical system compared to when viewed with the naked eye. Understanding how to calculate total magnification will increase your knowledge of optics and its applications in laboratories. Therefore, we need to understand what a microscope is. A microscope, otherwise known as a compound microscope is a tool that helps us to see microscopic objects (very tiny objects) that we cannot see with the naked eye.

There are different designs of microscopes today. However, you need to know that a microscope consists of a rack, eyepiece (ocular), stage, eyepiece tube (eyepiece holder), condenser, aperture, objective lenses, knobs, nose piece, and light source.

## How to Calculate Total Magnification

To calculate the total magnification of an optical system, you will need to multiply the magnification of each individual component in the system.

In other words, total magnification is the product of all magnifications along the light path from the object to the observer’s eye. We can also refer to the observer’s eye as a recording medium.

For example, if you have a microscope with an eyepiece that magnifies 10x, and an objective lens that magnifies 40x. The total magnification would be 10x multiplied by 40x to obtain 400x.

Therefore,

Total magnification = eyepiece x objective lens

## Understanding How to Calculate Total Magnification

Total magnification is typically expressed as a ratio or a factor, indicating how many times the image has been magnified in comparison to the actual size of the object. To calculate total magnification, you need to consider two factors:

1. Objective Lens Magnification: The objective lens is the lens closest to the object you are observing in the optical instrument. It provides the primary magnification. The magnification of the objective lens is usually marked on the lens itself, such as 4x, 10x, 40x, or 100x. This number represents the factor by which the objective lens enlarges the object.
2. Eyepiece (Ocular) Lens Magnification: The eyepiece lens, or ocular lens, is the lens through which you directly observe the magnified image. It contributes additional magnification. The eyepiece lens magnification is also marked, often as 10x.

To calculate the total magnification, you simply multiply the magnification of the objective lens by the magnification of the eyepiece lens:

Total Magnification = Objective Lens Magnification × Eyepiece Lens Magnification

For example, if you are using a microscope with a 40x objective lens and a 10x eyepiece lens, the total magnification would be:

Total Magnification = 40x (Objective) × 10x (Eyepiece) = 400x

So, in this case, the image of the object you are viewing through the microscope would appear 400 times larger than its actual size.

### Example 1

Thus, assuming

objective lens = 10x

Then

Total magnification = 10x * 10x = 20x

### Example 2

With the object’s lens as 4x

Total magnification = eyepiece (ocular) x object’s lens

Which implies that the total magnification = 10x * 4x = 40x

Note: It is important to know that the power of the eyepiece is usually 10x. Additionally, the total magnification can vary depending on the combination of lenses and other optical components used in the optical system. It’s also dependent on the distance between the components and the object under observation.

The magnification of objective lenses are 4x, 10x, and 40x.

## Note

Total magnification is a very important parameter when using optical instruments. This is because it determines the level of detail you can observe and the size of objects you can effectively study. Additionally, It allows scientists, researchers, and students to understand the micro and macro worlds with precision and clarity, making it an essential concept in fields such as biology, materials science, and astronomy.

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Source:

Byjus