Give the ratio of velocities of light rays of wavelength 4000Å and 8000Å in vacuum.

Answer

To solve the problem of finding the ratio of velocities of light rays of wavelength 4000 Å and 8000 Å in vacuum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Wavelengths**:
- Let the wavelength of the first light ray be \( \lambda_1 = 4000 \, \text{Å} \).
- Let the wavelength of the second light ray be \( \lambda_2 = 8000 \, \text{Å} \).

2. **Understand the Concept of Speed of Light in Vacuum**:
- In a vacuum, the speed of light is constant and is denoted by \( c \). The value of \( c \) is approximately \( 3 \times 10^8 \, \text{m/s} \).

3. **Determine the Velocities of the Light Rays**:
- Since both light rays are traveling in a vacuum, their velocities will be equal to the speed of light:
- \( V_1 = c \) for the first light ray (4000 Å).
- \( V_2 = c \) for the second light ray (8000 Å).

4. **Calculate the Ratio of Velocities**:
- The ratio of the velocities \( V_1 \) and \( V_2 \) can be expressed as:
\[ \frac{V_1}{V_2} = \frac{c}{c} = 1 \]
- Therefore, the ratio of the velocities of the light rays is:
\[ V_1 : V_2 = 1 : 1 \]

5. **Conclusion**:
- The final answer is that the ratio of the velocities of the light rays of wavelengths 4000 Å and 8000 Å in vacuum is \( 1 : 1 \).