When two or more lnses of magnification `m_(1) ,m_(2), m_(3)` are kept in contact, the total magnification (m) produced is given by

Options

A. `m=m_(1)+m_(2)+m_(3)+...+`
B. `m=m_(1)+m_(2)-m_(3)-m_(4)...`
C. `m=(m_(1)m_(2))/(m_(3))+(m_(2)m_(4))/(m_(4))+....`
D. `m= m_(1) xx m_(2) xx m_(3) xx ...`

Answer

To find the total magnification (M) produced by two or more lenses of magnification \( m_1, m_2, m_3 \) kept in contact, we can follow these steps:

### Step 1: Understand the Definition of Magnification
Magnification (M) is defined as the ratio of the height of the image (B) to the height of the object (U). For each lens, we can express magnification as:
- For the first lens: \( m_1 = \frac{B_1}{U_1} \)
- For the second lens: \( m_2 = \frac{B_2}{U_2} \)

### Step 2: Combine the Magnifications
When two lenses are placed in contact, the total magnification produced by the combination of these lenses can be calculated by multiplying their individual magnifications:
\[ M = m_1 \times m_2 \]

### Step 3: Generalize for Multiple Lenses
If there are more than two lenses, say three lenses with magnifications \( m_1, m_2, m_3 \), the total magnification can be expressed as:
\[ M = m_1 \times m_2 \times m_3 \]

### Step 4: Conclusion
Thus, the total magnification (M) produced by two or more lenses kept in contact is given by the product of their individual magnifications:
\[ M = m_1 \times m_2 \times m_3 \]

### Final Answer
The total magnification \( M \) is given by:
\[ M = m_1 \times m_2 \times m_3 \]

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