The magnification or magnifying power of a microscope, M, is defined as by how much larger the image formed by the microscope is in relation to the real object being viewed through the microscope. The angular extend of these two are compared when they are situated at the near point, nP, of the eye.
o represents the object in the drawing, in this case the divisions on a steel ruler, and i the enlarged virtual image of the vernier caliper scale division as produced by the microscope. Both must be the same distance from the eye, usually at the near point. This was done by checking that there is no parallax between them - http://www.lhup.edu/~dsimanek/scenario/labman3/thinlens.htm
The magnification is then given by
M = θ`/ θ
For small angles this reduces to
M = h`/h
with h and h` being the linear dimensions or height of the object and image.
Step 1: Setup
The magnification of a travelling microscope was determined in this case. The object which was viewed through it was the scale on a vernier caliper. The divisions was 1/40th of an inch apart. These were compared with the millimeter scale on a steel ruler.
I found it difficult to eliminate parallax between the images of the ruler and the vernier scale using a clear microscope glass slide due to double images of the ruler being formed by reflections off the front and rear surfaces of the glass slide. This can be avoided by replacing the glass slide with a small mirror. One should position the mirror so that you can look over the top edge of the mirror through the microscope, but light from the ruler is still reflected into the eye by the mirror. Another option is to use a half-silvered mirror in which case one can look through the mirror into the microscope.
Step 2: Measurements
I found that about 13.8 ± 0.5 mm of the ruler divisions stretched over one of the vernier caliper divisions.
Step 3: Results
The magnification of the microscope is then
13.8 mm/(1/40 inch) x 1 inch /25.4 mm
= 13.8 x 40/25.4
with a limiting error of 0.8
The magnification is therefore approximately x22