Question

Students in a biology laboratory were asked to view certain cells microscopically and measure the size of a single cell. They were given a compound microscope with an eyepiece of 15X magnification and an objective lens of 10X magnification. The eyepiece has a scale with a least count of 10 um. When the students focused the cells under the given microscope, they found that one cell measured 60 divisions on the eyepiece scale. What is the approximate size of that cell (in um)?

• A. 0.47
• B. 2.8
• C. 4.0
• D. 24

Answer 1

Answer: (C)

4.0

Answer 2

To determine the actual size of the cell, we need to consider the total magnification of the microscope and the calibration of the eyepiece scale.

1. Calculate the Total Magnification:
   The total magnification of a compound microscope is the product of the eyepiece magnification and the objective lens magnification.
   Eyepiece Magnification = 15X
   Objective Lens Magnification = 10X
   Total Magnification ($M_{total}$) = Eyepiece Magnification × Objective Lens Magnification
   $M_{total} = 15 \times 10 = 150X$

2. Determine the Image Size of the Cell:
   The eyepiece has a scale with a least count of 10 um. This means that each division on the eyepiece scale corresponds to 10 um at the intermediate image plane (where the eyepiece reticle is located).
   The cell measured 60 divisions on the eyepiece scale.
   Image Size of the cell = Number of divisions × Least count per division
   Image Size of the cell = 60 divisions × 10 um/division
   Image Size of the cell = 600 um

3. Calculate the Actual Size of the Cell:
   The magnification relates the actual size of the object to its magnified image size.
   Total Magnification = Image Size / Actual Size
   Rearranging the formula to find the Actual Size:
   Actual Size = Image Size / Total Magnification
   Actual Size = 600 um / 150
   Actual Size = 4 um

Therefore, the approximate size of the cell is 4 um.