Video Transcript
A student drew an animal cell they had observed under the microscope. The diameter of the cell they drew was 100 millimeters, but the actual size of the
cell was 0.01 millimeters. How many times larger was the drawing than the actual cell?
In this question, we are talking about a drawing being larger than the object being
drawn, which means the image is magnified. The student was able to draw the cell because they used a microscope that magnifies
the cell’s image so it can be seen.
Magnification is the process by which an object is made larger in appearance. When a microscope magnifies an object, it uses magnifying lenses to do so. There are usually two magnifying lenses used in the common light microscope. The lens nearest the object is called the objective lens, and the lens that is being
looked through is the eyepiece lens.
To look at a cell, it needs to be put onto a glass slide. The slide is then put onto the stage and light is shone up from a source below
through the object on the slide. The light rays then enter the objective lens, which bends them, forming a magnified
image. The light rays then pass from this image through the eyepiece lens, magnifying the
image further. When we look through the eyepiece, we see this final magnified image. The magnification of each lens is marked on the side of it.
The common school microscope has three or four objective lenses from 4 times through
to 100 times and an eyepiece lens, which is usually of 10 times magnification. The total magnification of the object is calculated by multiplying the magnification
of the eyepiece lens by the magnification of the objective lens being used. So, if we were using the lowest-power objective lens, the magnification would be 10
times four, which equals 40. If using the highest-power objective lens, it would be 10 multiplied by 100, which
gives us a magnification of 1,000 times.
So, if we used the highest-power objective lens to look at an object 0.02 millimeters
in diameter, what size would the final image be? To work out how to calculate this, let’s use the magnification equation triangle. To use this, we just cover the variable we want to find out, here the size of the
image. This leaves us with 𝐴 multiplied by 𝑀, which means that the diameter of the actual
object multiplied by the total magnification equals the diameter of the image. If we look at this example, we multiply the diameter of the actual object, 0.02
millimeters, by the total magnification, 1,000. This gives us a final image diameter of 20 millimeters.
If we were asked to work out the magnification from the size of the object and the
size of the image, how would we calculate this? Well, we want to calculate the total magnification. So, we want this on its own on one side of the equal sign. We therefore need to rearrange the formula. At the moment, the magnification is multiplied by the diameter of the actual
object. To get rid of this, to leave magnification on its own, we have to do the opposite of
multiplying, which is dividing. So, we divide the left side by the diameter of the actual object.
The rule with equations is that whatever you do to one side, you do to the other to
keep it balanced. Therefore, we also need to divide the right-hand side by the diameter of the actual
object. On the left-hand side of the equation, the diameter of the actual object on the top
and bottom cancel out. We are then left with the equation total magnification equals diameter of image
divided by diameter of actual object. This is also shown in the magnification triangle. If you cover over the 𝑀 for magnification, you are left with 𝐼, diameter of image,
over 𝐴, diameter of actual object.
Let’s look at an example. If the diameter of the image is 50 millimeters and the diameter of the actual object
is 0.01 millimeters, we can put them into our equation, like so. This means that the total magnification is 50 divided by 0.01, which is 5,000
times. This equation can also be used for calculating how many times larger a drawing is
than an actual object. The diameter of the image is the diameter of the drawing.
Using this equation, we can now answer our question. It asks if the diameter of the drawing was 100 millimeters, but the actual size of
the cell was 0.01 millimeters, how many times larger was the drawing than the actual
cell? So, let’s put 100 millimeters for the diameter of the drawing and 0.01 millimeters
for the diameter of the actual object, the cell, into the equation. 100 millimeters divided by 0.01 millimeters gives us the answer, which is 10,000
times.
