How to Calculate the Total Magnification Power of a Compound Microscope?

Correct Answer: 1000×

The correct answer is 1000×. The total magnification power of a compound microscope is calculated by multiplying the magnification produced by the objective lens by the magnification produced by the eyepiece or ocular lens.

In this question, the objective lens has a magnification power of 100×, while the eyepiece has a magnification power of 10×. Therefore, the total magnification of the compound microscope is obtained by multiplying these two values.

Formula for Total Magnification of a Compound Microscope

The total magnification power of a compound microscope can be calculated using the following formula:

Total Magnification = Magnification of Objective Lens × Magnification of Eyepiece Lens

For the values given in the question:

Magnification of Objective Lens = 100×

Magnification of Eyepiece Lens = 10×

Substituting these values into the formula:

Total Magnification = 100 × 10

Total Magnification = 1000×

Therefore, the magnification power of the compound microscope is 1000×.

Why Are the Magnifications of the Objective and Eyepiece Multiplied?

A compound microscope is called a compound microscope because it uses more than one lens system to magnify an object. The two major lens systems involved in producing the final magnified image are the objective lens and the eyepiece lens, which is also known as the ocular lens.

The objective lens first produces a magnified image of the specimen. This magnified intermediate image is then viewed through the eyepiece, which magnifies it again. Since the image is magnified in two successive stages, the magnification values of the two lens systems are multiplied rather than added.

For example, if the objective lens enlarges a specimen 100 times and the eyepiece enlarges the resulting image another 10 times, the final image appears 1000 times larger than the original specimen. This is why the total magnification is calculated as 100 × 10 = 1000×.

Understanding the Role of the Objective Lens

The objective lens is the lens located closest to the specimen being observed. It is one of the most important components of a compound microscope because it produces the first magnified image of the specimen and plays a major role in determining image detail and resolution.

Most compound light microscopes contain several objective lenses mounted on a rotating nosepiece. Common objective lens magnifications include 4×, 10×, 40× and 100×. The user can rotate the nosepiece to select the objective lens required for a particular observation.

What Does a 100× Objective Lens Mean?

A 100× objective lens magnifies the specimen one hundred times during the first stage of image formation. This is a very high-power objective lens and is commonly called the oil immersion objective.

When a 100× objective is used with a standard 10× eyepiece, the total magnification becomes 1000×. This combination is commonly used to observe very small biological structures, including bacteria and fine cellular details that cannot be examined effectively at lower magnifications.

The 100× objective is commonly used with immersion oil because the oil helps reduce the loss of light caused by refraction between the glass slide and the objective lens. This allows more light to enter the objective and improves the numerical aperture and resolving ability of the microscope.

Understanding the Role of the Eyepiece or Ocular Lens

The eyepiece, also called the ocular lens, is the lens through which the observer looks. Its main function is to magnify the intermediate image already formed by the objective lens.

A standard compound microscope commonly has a 10× eyepiece. This means that the image produced by the objective lens is magnified another ten times before it reaches the observer’s eye.

In the present question, the objective lens first produces a 100-fold magnified image. The 10× ocular lens then magnifies that image another ten times. Therefore, the final image is magnified by a total factor of 1000.

Step-by-Step Calculation of Microscope Magnification

Step 1: Identify the Magnification of the Objective Lens

The question states that the magnification power of the objective lens is:

Objective Magnification = 100×

Step 2: Identify the Magnification of the Eyepiece

The magnification power of the eyepiece or ocular lens is:

Eyepiece Magnification = 10×

Step 3: Apply the Total Magnification Formula

The total magnification of a compound microscope is:

Total Magnification = Objective Magnification × Eyepiece Magnification

Step 4: Substitute the Given Values

Total Magnification = 100 × 10

Step 5: Calculate the Final Magnification

Total Magnification = 1000×

Thus, the final image viewed through the microscope is theoretically magnified 1000 times relative to the original specimen.

Why Is the Answer Not 110×?

A possible incorrect calculation would be to add the magnification of the objective lens and the eyepiece lens:

100 + 10 = 110×

However, this calculation is incorrect because the two lenses do not magnify the specimen independently and then combine their values by addition. Instead, the objective lens first magnifies the specimen, and the eyepiece then magnifies the already enlarged image.

Because magnification occurs sequentially in two stages, the values must be multiplied. Therefore, the correct calculation is 100 × 10 = 1000×, not 100 + 10 = 110×.

How Does a Compound Microscope Produce Magnification?

A compound microscope produces magnification through a two-stage image formation process. In the first stage, light passing through or reflected from the specimen enters the objective lens. The objective lens forms a magnified intermediate image inside the microscope.

In the second stage, the observer views this intermediate image through the eyepiece lens. The eyepiece acts as an additional magnifying lens and enlarges the image formed by the objective. The combined effect of these two lens systems produces the total magnification of the microscope.

This two-stage magnification system is the fundamental reason why a compound microscope can produce much greater magnification than a simple microscope that uses only a single lens system.

Examples of Total Magnification at Different Objective Powers

If a compound microscope has a standard 10× eyepiece, the total magnification changes according to the objective lens being used. With a 4× objective, the total magnification is 40×. With a 10× objective, the total magnification is 100×. With a 40× objective, the total magnification is 400×. Finally, with a 100× objective, the total magnification is 1000×.

These examples demonstrate that the eyepiece magnification remains constant while the total magnification changes when a different objective lens is selected.

Magnification and Resolution Are Not the Same

Although the question asks specifically about magnification, it is important to understand that magnification and resolution are different concepts in microscopy.

Magnification refers to how many times larger an image appears compared with the actual object. In this question, the microscope produces a total magnification of 1000×, meaning that the final image appears one thousand times larger than the original specimen.

Resolution, on the other hand, refers to the ability of a microscope to distinguish two closely spaced points as separate structures. Increasing magnification alone does not necessarily reveal additional details. If the resolving power of the optical system is insufficient, further enlargement produces a larger but blurred image.

Therefore, a good microscope must provide both adequate magnification and sufficient resolution. The 100× oil immersion objective is especially useful because, when used correctly with immersion oil, it can improve light collection and support the observation of fine structural details.

Significance of the 100× Objective and 10× Eyepiece Combination

The combination of a 100× objective lens and a 10× eyepiece lens is a standard high-magnification arrangement in compound light microscopy. It produces a total magnification of 1000×.

This magnification is commonly associated with the examination of very small specimens. In microbiology, for example, the 100× oil immersion objective is frequently used for observing stained bacterial cells because lower-power objectives may not provide sufficient image detail.

The calculation itself is straightforward, but understanding the two-stage process of image magnification is essential. The objective lens produces the primary magnified image, while the eyepiece magnifies that image further. Their combined effect determines the final magnification observed by the user.

Final Answer

Correct Answer: 1000×

The total magnification power of a compound microscope is calculated by multiplying the magnification of the objective lens by the magnification of the eyepiece or ocular lens.

Total Magnification = Objective Magnification × Eyepiece Magnification

Total Magnification = 100× × 10× = 1000×

Therefore, when a compound microscope uses a 100× objective lens and a 10× eyepiece, the total magnification power of the microscope is 1000×.