If frequency of light wave propagating in water is halved its, speed

Options

A. Is halved
B. is doubled
C. Remains same
D. Becomes four times

Answer

To solve the problem, we need to analyze how the speed of light in a medium (water, in this case) is affected by changes in frequency.

### Step-by-step Solution:

1. **Understand the relationship between speed, frequency, and wavelength**:
The relationship is given by the equation:
\[ v = f \lambda \]
where \( v \) is the speed of light in the medium, \( f \) is the frequency, and \( \lambda \) is the wavelength.

2. **Identify the change in frequency**:
According to the problem, the frequency \( f \) of the light wave is halved. Therefore, if the original frequency is \( f \), the new frequency \( f' \) will be:
\[ f' = \frac{f}{2} \]

3. **Determine the effect on wavelength**:
Since the speed of light in a medium is constant, if the frequency is halved, the wavelength must change to maintain the equation \( v = f \lambda \). We can express the new wavelength \( \lambda' \) as:
\[ v = f' \lambda' \implies v = \left(\frac{f}{2}\right) \lambda' \]
Rearranging gives:
\[ \lambda' = \frac{v}{f'} = \frac{v}{\frac{f}{2}} = \frac{2v}{f} = 2\lambda \]
This shows that the wavelength doubles when the frequency is halved.

4. **Conclusion about the speed of light in water**:
The speed of light in a medium (water) is determined by the properties of that medium, not by the frequency or wavelength of the light. Therefore, even though the frequency is halved and the wavelength is doubled, the speed \( v \) remains constant.

5. **Final Answer**:
The speed of light in water remains the same even if the frequency is halved.