A magician during a show makes a glass lens with n=1.47 disappear in a trough of liquid.
Refractive index of the liquid is

Options

A. 1.47
B. 1.33
C. `4//3`
D. `12//5`

Answer

To determine the refractive index of the liquid in which a glass lens with a refractive index of \( n = 1.47 \) disappears, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Disappearance**:
- A lens appears to disappear when it is placed in a medium with the same refractive index. This is because the light rays do not bend at the interface between the lens and the medium, making the lens effectively invisible.

2. **Identify the Refractive Index of the Lens**:
- The refractive index of the glass lens is given as \( n_{\text{lens}} = 1.47 \).

3. **Setting Up the Condition for Disappearance**:
- For the lens to disappear, the refractive index of the liquid \( n_{\text{liquid}} \) must be equal to the refractive index of the lens. This means:
\[ n_{\text{liquid}} = n_{\text{lens}} \]

4. **Substituting the Known Values**:
- Since \( n_{\text{lens}} = 1.47 \), we can substitute this value into our equation:
\[ n_{\text{liquid}} = 1.47 \]

5. **Conclusion**:
- Therefore, the refractive index of the liquid must be \( 1.47 \) for the glass lens to disappear.

### Final Answer:
The refractive index of the liquid is \( n = 1.47 \).

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