If a convex lens of refractive index `mu _l` is placed in a medium of refractive index `mu_m` Such that `mu_l > mu_m > mu_(air)` then

Options

A. The nature of the lens is diverging
B. The nature of the lens is converging
C. The nalure of the lens may be converging or diverging
D. The nature of the lens can't be determined

Answer

To determine the nature of a convex lens placed in a medium with a higher refractive index than air, we can follow these steps:

### Step 1: Understand the Properties of the Lens
A convex lens is characterized by its ability to converge light rays. The refractive index of the lens (μ_l) is greater than that of the medium (μ_m) in which it is placed, and both are greater than the refractive index of air (μ_air).

### Step 2: Use the Lens Maker's Formula
The lens maker's formula relates the focal length (f) of a lens to its refractive indices and the radii of curvature of its surfaces. The formula is given by:
\[ \frac{1}{f} = \left( \frac{\mu_l}{\mu_m} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
Where:
- \( \mu_l \) = refractive index of the lens
- \( \mu_m \) = refractive index of the medium
- \( R_1 \) and \( R_2 \) = radii of curvature of the lens surfaces

### Step 3: Analyze the Focal Length in Air
When the lens is in air, the focal length is positive since:
\[ \frac{1}{f} = \left( \frac{\mu_l}{\mu_{air}} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
Here, \( \mu_l > \mu_{air} \) implies that \( \frac{\mu_l}{\mu_{air}} - 1 > 0 \), leading to a positive focal length.

### Step 4: Analyze the Focal Length in the Medium
Now, when the lens is placed in a medium with refractive index \( \mu_m \):
\[ \frac{1}{f'} = \left( \frac{\mu_l}{\mu_m} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
Given that \( \mu_l > \mu_m \), we have \( \frac{\mu_l}{\mu_m} - 1 > 0 \). This means that \( f' \) will also be positive.

### Step 5: Conclusion
Since both focal lengths \( f \) and \( f' \) are positive, the lens behaves as a converging lens in both cases. Therefore, the nature of the lens remains converging when placed in a medium with a refractive index lower than that of the lens.

### Final Answer
The lens is a **converging lens**.

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