# A microscope has an objective lens with a focal length of 16.22 mm and an eyepiece with a focal length of 9.50 mm. With the length of the barrel set at 29.0 cm, the diameter of a red blood cell’s image subtends an angle of 1.43 mrad with the eye. It the final image distance is 29.0 cm from the eyepiece, what is the actual diameter of the red blood cell? Hint: To solve this question, go back to basics and use the thin-lens equation.

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300
Chapter 25, Problem 30P
Textbook Problem
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## A microscope has an objective lens with a focal length of 16.22 mm and an eyepiece with a focal length of 9.50 mm. With the length of the barrel set at 29.0 cm, the diameter of a red blood cell’s image subtends an angle of 1.43 mrad with the eye. It the final image distance is 29.0 cm from the eyepiece, what is the actual diameter of the red blood cell? Hint: To solve this question, go back to basics and use the thin-lens equation.

To determine
The actual diameter of the red blood cell.

### Explanation of Solution

The diameter of the final image is,

he=rθ

• r is the distance between the image and the eye
• θ is the angle subtended by the diameter of the image

Substitute 29.0cm for r and 1.43mrad for θ .

The required object distance for the eyepiece is,

pe=qefeqefe

• qe is the image distance for the eyepiece
• fe is the focal length of the eyepiece

Substitute 29.0cm for qe and 0.950cm for fe .

pe=(29.0cm)(0.950cm)29.0cm0.950cm=0.920cm

The magnification produced by the eyepiece is,

Me=qepe=(29.0cm)0.920cm=31.5

The image distance for the objective lens is,

q1=Lpe=29

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