The magnifying power of compound microscope in terms of the magnification `m_0` due to objective and magnifyging power `m_E` by the eye-piece is given by

Options

A. `(m_(0))/(m_(E))`
B. `m_(0)xxm_(E)`
C. `m_(0)+m_(E)`
D. `(m_(E))/(m_(0))`

Explanation

To find the magnifying power of a compound microscope in terms of the magnification \( m_0 \) due to the objective and the magnifying power \( m_E \) by the eyepiece, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Components**:
- A compound microscope consists of two lenses: the objective lens and the eyepiece (ocular lens).
- The objective lens is responsible for forming the first magnified image of the object, while the eyepiece further magnifies this image for the viewer.

2. **Magnification by the Objective**:
- When a small object is placed in front of the objective lens, it produces a magnified image. The magnification produced by the objective lens is denoted as \( m_0 \).

3. **Image as Object for Eyepiece**:
- The image formed by the objective lens acts as the object for the eyepiece. This means that the eyepiece will take this image and magnify it further.

4. **Magnification by the Eyepiece**:
- The eyepiece magnifies the image produced by the objective lens by a factor denoted as \( m_E \).

5. **Total Magnification**:
- The total magnification of the compound microscope is the product of the magnification due to the objective and the magnification due to the eyepiece. Therefore, the total magnifying power \( M \) of the compound microscope can be expressed as:
\[ M = m_0 \times m_E \]

### Final Answer:
The magnifying power of the compound microscope is given by:
\[ M = m_0 \times m_E \]

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