A completely transparent material will be invisible in vacuum when its refractive index `mu` is

Options

A. unity
B. less than unity
C. more than unity
D. infinity

Explanation

To determine the refractive index `μ` at which a completely transparent material becomes invisible in a vacuum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Refractive Index**:
- The refractive index (μ) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v). Mathematically, it is expressed as:
\[ μ = \frac{c}{v} \]

2. **Refractive Index of Vacuum**:
- The refractive index of vacuum is defined to be 1 (μ_vacuum = 1).

3. **Condition for Invisibility**:
- For a material to be invisible in a vacuum, the refractive index of the material must match the refractive index of its surroundings (in this case, vacuum). This means that the refractive index of the material must also be 1.

4. **Reasoning Behind Invisibility**:
- When light travels from one medium to another, refraction occurs if there is a change in the refractive index. If both the material and the surrounding medium (vacuum) have the same refractive index (1), there will be no bending of light (no refraction) at the interface. Consequently, the material will not reflect or refract light, making it invisible.

5. **Conclusion**:
- Therefore, the refractive index `μ` at which a completely transparent material will be invisible in vacuum is:
\[ μ = 1 \]

### Final Answer:
A completely transparent material will be invisible in vacuum when its refractive index `μ` is **1**.

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