Question

A microorganism viewed under a microscope with 40X objective and 10X eyepiece measures 4000µm. The same microorganism observed under a dissecting microscope with a 10X lens would measure
A. 40µm
B. 100µm
C. 10µm
D. 400µm

Answer 1

Hint: To observe microorganisms, we need to increase our maximum magnification and resolution. Magnification and resolution both are different terms. Magnification describes how many times bigger an image gets when it is kept under a microscope and resolution, describes how much detail we can see in the picture.

Formula used: To find the size of the image, we figure out the size of the specimen and total magnification by using the formula - $\text{magnification=}{\displaystyle \frac{\text{size of the image}}{\text{size of specimen}}}$

Complete step by step answer: As we knew, dissection microscopes have less magnification than a compound microscope. Compared to compound microscopes which have several lenses, dissection microscopes only have one set of lenses. 10X magnification is the most common in dissecting microscopes.
To calculate total magnification, how much your image (or) your specimen is being magnified (or) increased, you should multiply eyepiece magnification by the objective lens magnification.
Here, the eyepiece magnification is 10X and the objective magnification is 40X the total magnification will be 400X.

$\Rightarrow$ $\text{magnification=}{\displaystyle \frac{\text{size of the image}}{\text{size of specimen}}}$

$\Rightarrow$$\text{400X=}{\displaystyle \frac{\text{4000 }\mu \text{ m}}{\text{size of specimen}}}$

$\Rightarrow$$\text{size of specimen =}{\displaystyle \frac{\text{4000 }\mu \text{ m}}{\text{400X}}}\text{=10 }\mu \text{ m}$

Now, we have the size of the specimen that is 10 µm. By using this we calculate the size of the image in the dissection microscope.

Using the same formula: $\text{magnification=}{\displaystyle \frac{\text{size of the image}}{\text{size of specimen}}}$

Here, 10X is the total magnification of the Dissecting microscope.
$\Rightarrow$$\text{10X=}{\displaystyle \frac{\text{size of image}}{\text{10 }\mu \text{ m}}}$

$\Rightarrow$$\text{size of image = }\left(\text{10X}\right)\left(\text{10 }\mu \text{ m}\right)$

$\Rightarrow$ Size of image = 100 µm

Hence, the size of the image in the dissection microscope is 100 µm, i.e., Option-B is the correct answer.

Note: Commonly, the microscope we use in the class is a compound microscope. It magnifies the specimen with an objective lens and with an ocular eyepiece but in dissection, they do not have more lens and will have total magnification written on the knob, so that you will not require to do multiplication to resolve it.