A convex lens made up of glass of refractive index `1.5` is dippedin turn
(i) in a medium of refractive index `1.65`
(ii) in a medium of refractive index `1.33`
(a) Will it behave as converging or diverging lens in the two cases ?
(b) How will its focal length changes in the two media ?

Explanation

To solve the problem step by step, we will analyze the behavior of a convex lens made of glass with a refractive index of 1.5 when it is placed in two different media with refractive indices of 1.65 and 1.33.

### Step 1: Understanding Lens Behavior
A convex lens is typically a converging lens in air (or vacuum) because its refractive index is greater than that of air (which is approximately 1). The behavior of the lens (whether it converges or diverges light) depends on the relative refractive indices of the lens material and the surrounding medium.

### Step 2: Case (i) - Medium with Refractive Index 1.65
1. **Calculate the relative refractive index**:
- The refractive index of the lens (n_lens) = 1.5
- The refractive index of the medium (n_medium) = 1.65
- The relative refractive index (n_relative) = n_lens / n_medium = 1.5 / 1.65

2. **Determine the behavior**:
- Since n_relative < 1, the term (n_relative - 1) will be negative.
- This indicates that the lens will behave as a diverging lens in this medium.

### Step 3: Case (ii) - Medium with Refractive Index 1.33
1. **Calculate the relative refractive index**:
- The refractive index of the medium (n_medium) = 1.33
- The relative refractive index (n_relative) = n_lens / n_medium = 1.5 / 1.33

2. **Determine the behavior**:
- Since n_relative > 1, the term (n_relative - 1) will be positive.
- This indicates that the lens will behave as a converging lens in this medium.

### Step 4: Focal Length Changes
1. **Focal length in air**:
- The focal length in air (f) can be determined using the lens maker's formula, but we will focus on the relative changes in focal length.
- In air, the lens behaves as a converging lens, and we can assume a positive focal length.

2. **Focal length in medium 1 (n = 1.65)**:
- Using the formula: \( \frac{1}{f_1} = (n_lens/n_medium - 1) \cdot \frac{1}{f} \)
- Since \( n_lens/n_medium < 1 \), \( f_1 \) will be negative, indicating a diverging focal length.

3. **Focal length in medium 2 (n = 1.33)**:
- Using the same formula: \( \frac{1}{f_2} = (n_lens/n_medium - 1) \cdot \frac{1}{f} \)
- Since \( n_lens/n_medium > 1 \), \( f_2 \) will be positive, indicating a converging focal length.

### Summary of Results
(a) In the medium of refractive index 1.65, the lens behaves as a diverging lens. In the medium of refractive index 1.33, it behaves as a converging lens.

(b) The focal length becomes negative in the medium of refractive index 1.65 (diverging lens) and remains positive in the medium of refractive index 1.33 (converging lens).