If the real depth of a coin in water (`mu` = 4/3) is 4 cm, the apparent depth is

Options

A. 3 cm
B. `1/3` cm
C. `16/3`
D. None of these

Answer

To find the apparent depth of a coin submerged in water, we can use the formula that relates the real depth, apparent depth, and the refractive index of the medium.

### Step-by-step Solution:

1. **Identify the given values**:
- Real depth (d) = 4 cm
- Refractive index (μ) = 4/3

2. **Recall the formula**:
The relationship between real depth (d), apparent depth (d'), and refractive index (μ) is given by:
\[ \mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} \]
This can be rearranged to find the apparent depth:
\[ \text{Apparent Depth} = \frac{\text{Real Depth}}{\mu} \]

3. **Substitute the values into the formula**:
\[ \text{Apparent Depth} = \frac{4 \text{ cm}}{\frac{4}{3}} \]

4. **Simplify the expression**:
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \text{Apparent Depth} = 4 \text{ cm} \times \frac{3}{4} \]

5. **Calculate the apparent depth**:
\[ \text{Apparent Depth} = 3 \text{ cm} \]

### Final Answer:
The apparent depth of the coin in water is **3 cm**.

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