In a compound microscope the objective of `f_(o)` and eyepiece of `f_(e)` are placed at distance `L` such that `L` equals

Options

A. `f_(o)+f_(e)`
B. `f_(0)-f_(e)`
C. Much greater than `f_(0)` or `f_(e)`
D. Need not depend either value of focal lengths

Answer

To find the distance \( L \) between the objective lens and the eyepiece in a compound microscope, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A compound microscope consists of two convex lenses: the objective lens (with focal length \( f_o \)) and the eyepiece (with focal length \( f_e \)).
- The objective lens is placed close to the object, and the eyepiece is placed near the eye of the observer.

2. **Image Formation by Objective Lens**:
- The objective lens forms a real, inverted, and magnified image of the object. Let’s denote the distance between the objective lens and the eyepiece as \( L \).
- The distance \( L \) can be expressed in terms of the focal lengths of the lenses.

3. **Using Lens Formula**:
- For the objective lens, the image distance \( v_o \) and object distance \( u_o \) can be related using the lens formula:
\[ \frac{1}{f_o} = \frac{1}{v_o} - \frac{1}{u_o} \]
- The image formed by the objective lens acts as an object for the eyepiece.

4. **Image Formation by Eyepiece**:
- The eyepiece forms a virtual image, which is further magnified. The distance between the two lenses \( L \) can be expressed as:
\[ L = f_o + f_e \]
- This is because the total distance is the sum of the focal lengths of both lenses when they are in a compound microscope setup.

5. **Condition for L**:
- It is important to note that \( L \) must be much greater than either \( f_o \) or \( f_e \) to ensure proper functioning of the microscope.
- Therefore, we can state:
\[ L \gg f_o \quad \text{and} \quad L \gg f_e \]

6. **Final Expression**:
- Thus, the distance \( L \) can be summarized as:
\[ L = f_o + f_e \]
- This indicates that the distance between the two lenses in a compound microscope is the sum of their focal lengths.