Which of the following statements is correct?

Options

A. When a lens is dipped in water, magnitude of its focal length increases.
B. When a lens is dipped in water, magnitude of its focal length decreases
C. When a spherical mirror is dipped in water, magnitude of its focal length increases.
D. None of these.

Answer

To determine which of the statements is correct, we will analyze each statement one by one.

### Step 1: Analyze Statement A
**Statement A:** "When a lens is dipped in water, the magnitude of its focal length increases."

- The focal length \( f \) of a lens is given by the formula:
\[ \frac{1}{f} = \frac{\mu_2}{\mu_1} - 1 \left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]
where \( \mu_2 \) is the refractive index of the lens, \( \mu_1 \) is the refractive index of the medium, and \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces.

- When the lens is in air, \( \mu_1 \) is approximately 1. When it is dipped in water, \( \mu_1 \) increases (to approximately 1.33 for water).

- As \( \mu_1 \) increases, the term \( \frac{\mu_2}{\mu_1} - 1 \) decreases, leading to an increase in the focal length \( f \).

**Conclusion:** Statement A is correct.

### Step 2: Analyze Statement B
**Statement B:** "When a lens is dipped in water, the magnitude of its focal length decreases."

- From our analysis of Statement A, we found that the focal length actually increases when the lens is dipped in water.

**Conclusion:** Statement B is incorrect.

### Step 3: Analyze Statement C
**Statement C:** "When a spherical mirror is dipped in water, the magnitude of its focal length increases."

- The focal length of a spherical mirror is given by the formula:
\[ f = \frac{R}{2} \]
where \( R \) is the radius of curvature. The focal length of a mirror does not depend on the refractive index of the medium because reflection is a surface phenomenon.

- Thus, dipping a mirror in water does not affect its focal length.

**Conclusion:** Statement C is incorrect.

### Step 4: Analyze Statement D
**Statement D:** "None of these."

- Since we have determined that Statement A is correct, Statement D is also incorrect.

### Final Conclusion
The correct statement is **Statement A**: "When a lens is dipped in water, the magnitude of its focal length increases."

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