# How Do You Calculate the Actual Diameter of a Red Blood Cell Using a Microscope?

• katierob
In summary, using the given focal lengths and barrel length of a microscope, the diameter of a red blood cell's image can be calculated by using the ratio of the image height to its distance from the eye. The angle subtended by the image with the eye is a small angle, which can be used to calculate the image height. By substituting the values into the equation, the actual diameter of the red blood cell can be determined. However, it is important to check notation and units to ensure accuracy.
katierob

## Homework Statement

A microscope has an objective lens with a focal length of 16.22 mm and an eyepiece with a focal length of 9.30 mm. With the length of the barrel set at 25.0 cm, the diameter of a red blood cell's image subtends an angle of 1.43 mrad with the eye. If the final image distance is 25.0 cm from the eyepiece, what is the actual diameter of the red blood cell?
h1 =

m=-L/Fo(25cm/Fe)
m=hi/ho

## The Attempt at a Solution

I can't figure out how to get the object height without the image height? I think it has something to do with the angle at which the image subtends with the eye, but I don't have an equation for that, so I don't know where to go once I get m.

For small angles, the angle is the ratio of the height of the image to its distance from the eye. This comes from the definition of an angle (in radians) as the ratio of arc length to radius. If you know how far the image is from the eye, you can calculate its height from the angle.

thanks, so I tried this again using the ratio you gave above, but it still isn't coming out right, here's what I did:
m=-(25/1.622)(25/.93)=-414.3298463
height of the image=(1.43e-3)(25cm)=.03575
height of the object=(.03575) / (-414.3298463) = -.86283912e-6 meters
why is this incorrect?

katierob said:
thanks, so I tried this again using the ratio you gave above, but it still isn't coming out right, here's what I did:
m=-(25/1.622)(25/.93)=-414.3298463
height of the image=(1.43e-3)(25cm)=.03575
height of the object=(.03575) / (-414.3298463) = -.86283912e-6 meters
why is this incorrect?

## What is the purpose of adjusting the height of an object under a microscope?

Adjusting the height of an object under a microscope allows for better focusing and clarity of the image. It also allows for the examination of different parts of the specimen at different focal planes.

## How do you measure the height of an object under a microscope?

The height of an object under a microscope can be measured using the fine adjustment knobs on the microscope. These knobs move the stage up or down, allowing for precise measurements of the object's height.

## What is the relationship between the object height and magnification under a microscope?

The object height and magnification under a microscope are directly proportional. As the magnification increases, the object height appears larger and more detailed in the field of view.

## What happens if the object height is too high or too low under a microscope?

If the object height is too high, the image may appear blurry or out of focus. If the object height is too low, the image may not be visible at all. It is important to adjust the object height carefully for optimal imaging.

## Can the height of an object be adjusted under all types of microscopes?

Yes, the height of an object can be adjusted under all types of microscopes, including compound, stereo, and electron microscopes. However, the method for adjusting the height may differ depending on the type of microscope.

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