Question

A microscope with an overall magnification of 800 has an objective that magnifies by 200.

(a) What is the magnification of the eyepiece?

(b) If there are two other objectives that can be used, having magnifications of 100 and 400, what other total magnifications are possible?

Short answer

1. The magnification of the eyepiece is 4.
2. The other possible total magnifications are 400 and 1600.

Step-by-step solution

Step 1: What does magnification mean on a microscope?

A microscope's ability to produce a picture of an object at a scale greater (or even smaller) than its actual size is known as magnification. Magnification is only beneficial when it is feasible to see more details of an object in a picture than when looking at it with the unaided eye.

Given information and Formula to be used(a)

$$\begin{gathered} m_{total}=800 \\ {m}_{obj}=200 \end{gathered}$$$$\begin{gathered} m_{total}=800 \\ {m}_{obj}=200 \end{gathered}$$

The magnification of the eyepiece can be obtained using the expression,

$$\begin{gathered} m_{total}=m_{obj}{m}_{eyepiece} \\ {m}_{eyepiece}=\frac{m_{total}}{m} \end{gathered}$$…………..(1)

Substitute the given data in the above expression will give,

$m_{eyepiece}=4$

Therefore, the eyepiece's magnification is 4.

What other total magnifications are possible? (b)

For the first objective ${m^1}_{obj}$ gets,

$$\begin{gathered} {m^1}_{obj}=100\times \left(4\right) \\ =800 \end{gathered}$$

For the second objective role="math" localid="1654000885859" ${m^2}_{obj}$ gets,

$$\begin{gathered} {m^2}_{obj}=400\times \left(4\right) \\ =1600 \end{gathered}$$

Therefore, the other total magnifications are 400 and 1600.