A glass piece is dipped in a liquid of refractive index `(4)/(3)` it gets disappeared in the liquid. The refractive index of the glass piece is?

Options

A. `(3)/(4)`
B. `(5)/(3)`
C. `(4)/(5)`
D. `(4)/(3)`

Explanation

To find the refractive index of the glass piece that disappears in a liquid with a known refractive index, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Refraction**:
- When an object is placed in a medium, it becomes visible or invisible based on the difference in refractive indices between the object and the medium. If the refractive indices are the same, the object becomes invisible.

2. **Identify Given Information**:
- The refractive index of the liquid is given as \( \frac{4}{3} \).

3. **Apply the Condition for Disappearance**:
- Since the glass piece disappears in the liquid, we conclude that the refractive index of the glass piece must be equal to the refractive index of the liquid.

4. **Set Up the Equation**:
- Let the refractive index of the glass piece be \( n_g \).
- According to the condition for disappearance, we have:
\[ n_g = n_l \]
- Where \( n_l \) is the refractive index of the liquid.

5. **Substitute the Known Value**:
- We know that \( n_l = \frac{4}{3} \).
- Therefore, substituting this value into our equation gives:
\[ n_g = \frac{4}{3} \]

6. **Conclusion**:
- The refractive index of the glass piece is \( \frac{4}{3} \).

### Final Answer:
The refractive index of the glass piece is \( \frac{4}{3} \).

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