If the eyepiece lens magnifies 10 times, what objective lens will give 400X magnification?

Options

A. 0.4 X
B. 4 X
C. 40X
D. 400X

Answer

To solve the problem of determining the required objective lens magnification to achieve a total magnification of 400X when the eyepiece lens magnifies 10 times, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components of Magnification**:
- The total magnification of a microscope is the product of the magnification of the eyepiece lens (ME) and the objective lens (MO).
- The formula for total magnification is:
\[ \text{Total Magnification} = \text{Eyepiece Magnification} \times \text{Objective Magnification} \]

2. **Identify the Given Values**:
- The magnification of the eyepiece lens (ME) is given as 10X.
- The desired total magnification is 400X.

3. **Set Up the Equation**:
- Using the formula for total magnification, we can write:
\[ 400X = 10X \times MO \]

4. **Solve for Objective Lens Magnification (MO)**:
- Rearranging the equation to isolate MO gives:
\[ MO = \frac{400X}{10X} \]
- Simplifying this:
\[ MO = 40X \]

5. **Conclusion**:
- The required magnification of the objective lens to achieve a total magnification of 400X when the eyepiece magnifies 10X is **40X**.

### Final Answer:
The objective lens should have a magnification of **40X**.

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