what is the field diameter if the ocular mag. is 10x and the objective mag. is 10x
The correct answer and explanation is:
To find the field diameter in a compound microscope setup when the ocular (eyepiece) magnification and objective magnification are given, we need to understand some basics first.
What is Field Diameter?
- The field diameter refers to the actual size of the area you can see when looking through the microscope.
- It is usually measured in micrometers (µm) or millimeters (mm).
- The field diameter depends on the field of view (FOV) of the microscope, which changes with the magnification.
Given:
- Ocular magnification = 10x
- Objective magnification = 10x
Step 1: Understand Total Magnification
The total magnification of a microscope is: Total Magnification=Ocular Magnification×Objective Magnification\text{Total Magnification} = \text{Ocular Magnification} \times \text{Objective Magnification}
So, 10×10=100×10 \times 10 = 100 \times
Step 2: Field Diameter and Magnification Relationship
The field diameter is inversely proportional to the total magnification. This means as magnification increases, the field diameter decreases.
The relationship can be written as: Field Diameter2=Magnification1×Field Diameter1Magnification2\text{Field Diameter}_2 = \frac{\text{Magnification}_1 \times \text{Field Diameter}_1}{\text{Magnification}_2}
Step 3: Applying the Formula
We need to know the field diameter at a reference magnification (usually the lowest power objective) to calculate the new field diameter.
For example, if the field diameter at 10x objective and 10x ocular (total 100x) is to be found but the reference is usually given at the lowest objective power (often 4x objective and 10x ocular), which might have a field diameter of around 4.5 mm (this value depends on the microscope model, but 4.5 mm is a common estimate).
Using the formula: Field Diameter at 100x=Field Diameter at 40x×40100\text{Field Diameter at 100x} = \frac{\text{Field Diameter at 40x} \times 40}{100}
Or more generally, if you know the field diameter at a lower magnification, you can find the new one.
Step 4: Estimation (If Reference Field Diameter is Unknown)
If no reference field diameter is given, you cannot calculate the exact field diameter just from magnifications.
However, microscopes often have ocular fields of view between 18 mm and 20 mm.
Using an example:
- Suppose the ocular field number (FN) is 18 mm.
- Field Diameter at total magnification MM is:
Field Diameter=Field Number (FN)M\text{Field Diameter} = \frac{\text{Field Number (FN)}}{M}
Here, total magnification M=10×10=100M = 10 \times 10 = 100.
So, Field Diameter=18 mm100=0.18 mm=180μm\text{Field Diameter} = \frac{18 \text{ mm}}{100} = 0.18 \text{ mm} = 180 \mu m
Summary:
- Total magnification = 10 (ocular) × 10 (objective) = 100x.
- If the ocular field number is 18 mm, field diameter = 18 mm / 100 = 0.18 mm.
- So, the field diameter is approximately 0.18 mm (180 micrometers) at 100x magnification.
Explanation (300 words):
The field diameter in a microscope indicates the size of the circular viewing area seen when looking through the eyepiece. It’s important because it helps estimate how much of the specimen you can observe at once. The field diameter changes inversely with the magnification: higher magnification means a smaller field of view, and lower magnification means a larger field of view.
In your case, the microscope has a 10x ocular lens and a 10x objective lens. The total magnification is the product of these two, which is 100x. To find the field diameter at this total magnification, you need a reference field diameter, usually provided by the manufacturer or measured at the lowest objective magnification (for example, 4x or 10x objectives).
If you know the ocular field number (FN), a standard measurement usually around 18 mm for common microscopes, the field diameter can be calculated by dividing this number by the total magnification. Here, with an FN of 18 mm and total magnification of 100x, the field diameter would be: 18 mm100=0.18 mm\frac{18 \text{ mm}}{100} = 0.18 \text{ mm}
This means that under these settings, the visible area diameter is 0.18 mm, or 180 micrometers.
This shrinking field diameter at higher magnifications limits how much of the specimen you can view at once but allows you to see more detail in that small area. Understanding the field diameter is useful for estimating the actual size of structures seen under the microscope.
If you want the exact field diameter for your microscope, check the ocular field number (often engraved on the eyepiece) or measure the field diameter at a known magnification and use the inverse proportionality formula to calculate for other magnifications.