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 µm. 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?

 

(A) 0.47 µm (B) 2.8 µm (C) 4.0 µm (D) 24 µm

 

Give DETAILED SOLUTION.

The given microscope has eyepiece of magnification 15X and objective lens of magnification 10X.

Therefore, the total magnification = 15 × 10 = 150X

Eyepiece has least count 10 mm and the cell measured 60 divisions on the eyepiece scale. This means that the field of view or the area occupied by the cell under the given magnification is 60 × 10 = 600 mm.

In order to calculate the actual size of the object, we need to divide the area occupied by the cell with the total magnification of the compound microscope.

Therefore,

Actual size of the cell = Area occupied (field of view)/Total magnification

                            = 600/150

                            = 4 mm

                            = 0.004 mm

The approximate size of the cell is 4 mm.