A microorganism, when viewed under a compound microscope with an objective lens of 40X and an eye piece of 10X magnification measured 4000 `mu` in length. The same microorganism when observed under a dissection microscope with a lens of 10X magnification would measure

Options

A. 40 `mu`
B. 100 `mu`
C. 10 `mu`
D. 400 `mu`

Answer

To solve the problem step by step, we will first determine the size of the microorganism when viewed under the dissection microscope with a 10X magnification.

### Step-by-Step Solution:

1. **Understand the Magnification of the Compound Microscope**:
- The total magnification of a compound microscope is calculated by multiplying the magnification of the objective lens by the magnification of the eyepiece.
- Given: Objective lens = 40X, Eyepiece = 10X.
- Total magnification = 40X * 10X = 400X.

2. **Use the Magnification Formula**:
- The formula for magnification is:
\[ \text{Magnification} = \frac{\text{Size of Image}}{\text{Size of Specimen}} \]
- Here, we know the size of the image (4000 µm) and the total magnification (400X).

3. **Calculate the Size of the Specimen**:
- Rearranging the formula gives us:
\[ \text{Size of Specimen} = \frac{\text{Size of Image}}{\text{Magnification}} \]
- Plugging in the values:
\[ \text{Size of Specimen} = \frac{4000 \, \mu m}{400} = 10 \, \mu m \]

4. **Determine the Size of the Image Under the Dissection Microscope**:
- Now, we will observe the same microorganism under a dissection microscope with a magnification of 10X.
- Using the magnification formula again:
\[ \text{Size of Image} = \text{Magnification} \times \text{Size of Specimen} \]
- Plugging in the values:
\[ \text{Size of Image} = 10X \times 10 \, \mu m = 100 \, \mu m \]

5. **Final Answer**:
- The size of the microorganism when observed under a dissection microscope with a 10X magnification would measure **100 µm**.