Light passes through a closed cylindrical tube containing a gas. If the gas is gradually pumped out, the speed of light inside the tube will

Options

A. 1.increase
B. 2.decrease
C. 3.remain constant
D. 4.first increases then decreases

Answer

To solve the question regarding the speed of light in a closed cylindrical tube containing gas and the effect of gradually pumping out the gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- Initially, the cylindrical tube contains a gas (e.g., air). The speed of light in any medium is affected by the medium's refractive index. In this case, the gas has a certain refractive index which causes the speed of light to be less than its maximum value.

2. **Refractive Index of the Gas**:
- The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v):
\[ n = \frac{c}{v} \]
- For air, the refractive index is slightly greater than 1, which means light travels slower in air than in vacuum.

3. **Pumping Out the Gas**:
- As the gas is gradually pumped out of the tube, the pressure decreases, and the density of the gas also decreases. Eventually, if enough gas is removed, a vacuum will be created inside the tube.

4. **Speed of Light in Vacuum**:
- In a vacuum, the refractive index is 1 (n = 1), which means the speed of light reaches its maximum value:
\[ v = c \]
- Therefore, as the gas is removed and a vacuum is formed, the speed of light will increase to its maximum value.

5. **Conclusion**:
- Thus, as the gas is gradually pumped out and a vacuum is created, the speed of light inside the tube will increase and ultimately reach the speed of light in vacuum.

### Final Answer:
The speed of light inside the tube will increase and reach its maximum value when the gas is completely pumped out, resulting in a vacuum.

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