A double convex lens of refractive index `m_(1)` is immersed in a liquid of refractive index `m_(2)`. This lens will act as:

Options

A. diverging lens If `m_(1) gt m_(2)`
B. diverging lens if `m_(1) lt m_(2)`
C. converging lens if `m_(1) = m_(2)`
D. converging lens if `m_(1) lt m_(2)`

Answer

To determine whether a double convex lens will act as a converging or diverging lens when immersed in a liquid, we can analyze the relationship between the refractive indices of the lens and the surrounding medium.

### Step-by-step Solution:

1. **Understanding the Lens and Medium**:
- A double convex lens is a lens that is thicker in the middle than at the edges. It is typically a converging lens when in air (or vacuum) because it brings parallel rays of light to a focus.

2. **Refractive Indices**:
- Let the refractive index of the lens be \( m_1 \) and the refractive index of the surrounding liquid be \( m_2 \).

3. **Focal Length Formula**:
- The focal length \( f \) of the lens in a medium can be determined using the formula:
\[ \frac{1}{f} = (m_1 - m_2) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
- Here, \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces.

4. **Condition for Converging Lens**:
- For the lens to act as a converging lens, the focal length \( f \) must be positive. This occurs when:
\[ m_1 > m_2 \]
- This means the refractive index of the lens must be greater than that of the surrounding medium.

5. **Condition for Diverging Lens**:
- Conversely, if the lens acts as a diverging lens, the focal length \( f \) will be negative. This occurs when:
\[ m_1 < m_2 \]
- In this case, the refractive index of the surrounding medium is greater than that of the lens.

6. **Conclusion**:
- Therefore, the lens will act as a converging lens when \( m_1 > m_2 \) and as a diverging lens when \( m_1 < m_2 \).

### Final Answer:
- The double convex lens will act as a diverging lens if \( m_1 < m_2 \).