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 understand the relationship between the speed of light, frequency, and wavelength in a medium. Let's break it down step by step.

### Step 1: Understand the relationship between speed, frequency, and wavelength
The speed of a wave (v) is given by the formula:
\[ v = f \lambda \]
where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.

### Step 2: Analyze the effect of halving the frequency
If the frequency \( f \) is halved, we can express this as:
\[ f' = \frac{f}{2} \]
where \( f' \) is the new frequency.

### Step 3: Determine the new wavelength
Since the speed of light in a medium is constant, we can rearrange the wave speed formula to find the new wavelength \( \lambda' \):
\[ v = f' \lambda' \]
Substituting the new frequency:
\[ v = \left(\frac{f}{2}\right) \lambda' \]

### Step 4: Relate the original and new wavelengths
Since the speed of light in water remains constant, we can set the two expressions for speed equal to each other:
\[ f \lambda = \left(\frac{f}{2}\right) \lambda' \]
Now, we can solve for \( \lambda' \):
\[ \lambda' = 2 \lambda \]
This shows that when the frequency is halved, the wavelength doubles.

### Step 5: Conclusion about speed
Since the speed of light in water is a property of the medium and does not change with frequency or wavelength, we conclude that:
- The speed of light in water remains the same, regardless of the change in frequency.

### Final Answer
The speed of the light wave propagating in water remains the same when the frequency is halved.

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