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

[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 =

Homework Equations

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.

 

[OlderDan]

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.

 

[katierob]

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?

 

[OlderDan]

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?

check your e-6