The ratio of velocities of light waves of wavelengths 2000 A and 3000 A in vacuum is

Options

A. `1:1`
B. `2:3`
C. `3//2`
D. none of these

Explanation

To solve the problem of finding the ratio of the velocities of light waves of wavelengths 2000 Å (angstroms) and 3000 Å in vacuum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Speed of Light in Vacuum**:
The speed of light in vacuum is a constant value, denoted as \( c \). This value is approximately \( 3 \times 10^8 \) meters per second (m/s).

2. **Identifying the Wavelengths**:
We have two wavelengths given:
- \( \lambda_1 = 2000 \) Å
- \( \lambda_2 = 3000 \) Å

3. **Speed of Light for Different Wavelengths**:
In vacuum, the speed of light does not depend on the wavelength. Therefore, regardless of the wavelength of the light wave, the speed remains the same.

4. **Calculating the Ratio of Velocities**:
Since the speed of light in vacuum is the same for both wavelengths, we can express the ratio of their speeds as:
\[ \text{Ratio} = \frac{v_1}{v_2} \]
where \( v_1 \) and \( v_2 \) are the speeds of light for wavelengths 2000 Å and 3000 Å, respectively. Since both are equal to \( c \):
\[ \text{Ratio} = \frac{c}{c} = 1 \]

5. **Final Result**:
Therefore, the ratio of the velocities of light waves of wavelengths 2000 Å and 3000 Å in vacuum is:
\[ \text{Ratio} = 1 : 1 \]