A thin lens is made of glass of refractive index 1.6. Both the surfaces of lens are convex. When this lens is dipped in water of refractive index `4//3` then the lens will behave like

Options

A. A rectangular slab of refractive index 1.2 kept in air
B. A prism of refractive index 1.2 kept in air
C. Convergent lens
D. Divergent lens

Explanation

To determine how a thin convex lens made of glass with a refractive index of 1.6 behaves when dipped in water with a refractive index of 4/3, we can follow these steps:

### Step 1: Understand the Lens Formula
The lens formula for a thin lens is given by:
\[ \frac{1}{f} = (n_{relative} - 1) \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]
where:
- \( f \) is the focal length of the lens,
- \( n_{relative} \) is the relative refractive index of the lens with respect to the medium,
- \( r_1 \) and \( r_2 \) are the radii of curvature of the lens surfaces.

### Step 2: Calculate the Relative Refractive Index
When the lens is in air, the relative refractive index \( n_{relative} \) is calculated as:
\[ n_{relative} = \frac{n_{lens}}{n_{medium}} \]
In air, \( n_{medium} = 1 \). Therefore, for the glass lens:
\[ n_{relative} = \frac{1.6}{1} = 1.6 \]

When the lens is dipped in water:
\[ n_{relative} = \frac{n_{lens}}{n_{medium}} = \frac{1.6}{\frac{4}{3}} = \frac{1.6 \times 3}{4} = \frac{4.8}{4} = 1.2 \]

### Step 3: Substitute into the Lens Formula
Now, substituting \( n_{relative} \) into the lens formula:
\[ \frac{1}{f} = (1.2 - 1) \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]
This simplifies to:
\[ \frac{1}{f} = 0.2 \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]

### Step 4: Analyze the Sign of the Focal Length
Since \( r_1 \) and \( r_2 \) are both positive for a convex lens, the term \( \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \) is also positive. Thus, \( 0.2 \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \) is positive.

This means:
\[ \frac{1}{f} > 0 \quad \Rightarrow \quad f > 0 \]
Thus, the focal length \( f \) is positive.

### Step 5: Conclusion
Since the focal length \( f \) is positive, the lens will continue to behave as a converging lens even when submerged in water.

### Final Answer
The lens will behave like a converging lens when dipped in water.

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