For a colour of light the wavelength for air is 6000 Å and in water the wavelength is 4500 Å . Then the speed of light in water will be

Options

A. `5.xx10^(14) m//s`
B. `2.25xx10^(8) m//s`
C. `4.0xx10^(8) m//s`
D. Zero

Answer

To find the speed of light in water given the wavelengths in air and water, we can follow these steps:

### Step 1: Understand the relationship between speed, wavelength, and frequency
The speed of light in a medium is given by the formula:
\[ V = f \lambda \]
where \( V \) is the speed of light in the medium, \( f \) is the frequency of the light, and \( \lambda \) is the wavelength of the light in that medium.

### Step 2: Identify the given values
- Wavelength in air (\( \lambda_{air} \)) = 6000 Å = \( 6000 \times 10^{-10} \) m = \( 6.0 \times 10^{-7} \) m
- Wavelength in water (\( \lambda_{water} \)) = 4500 Å = \( 4500 \times 10^{-10} \) m = \( 4.5 \times 10^{-7} \) m
- Speed of light in air (\( C \)) = \( 3 \times 10^8 \) m/s

### Step 3: Use the relationship between speed and wavelength
Since the frequency remains constant when light travels from one medium to another, we can set up the following relationship:
\[ \frac{V_{water}}{C} = \frac{\lambda_{water}}{\lambda_{air}} \]

### Step 4: Rearrange the equation to find \( V_{water} \)
From the above relationship, we can express the speed of light in water as:
\[ V_{water} = C \times \frac{\lambda_{water}}{\lambda_{air}} \]

### Step 5: Substitute the known values
Now we can substitute the known values into the equation:
\[ V_{water} = 3 \times 10^8 \, \text{m/s} \times \frac{4.5 \times 10^{-7} \, \text{m}}{6.0 \times 10^{-7} \, \text{m}} \]

### Step 6: Simplify the equation
Calculating the fraction:
\[ \frac{4.5 \times 10^{-7}}{6.0 \times 10^{-7}} = \frac{4.5}{6.0} = 0.75 \]

Now substituting this back into the equation:
\[ V_{water} = 3 \times 10^8 \, \text{m/s} \times 0.75 \]
\[ V_{water} = 2.25 \times 10^8 \, \text{m/s} \]

### Conclusion
Thus, the speed of light in water is:
\[ V_{water} = 2.25 \times 10^8 \, \text{m/s} \]

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