To find the wavelength of light in a medium like water, you can use the formula that relates the wavelengths in different media to the indices of refraction:
\[ \lambda_{medium} = \frac{\lambda_{vacuum}}{n} \]
Where:
- \(\lambda_{medium}\) is the wavelength in the medium (water in this case),
- \(\lambda_{vacuum}\) is the wavelength in vacuum (589 nm for this light ray),
- \(n\) is the index of refraction of the medium (for water, \(n \approx 1.33\)).
Now, plug in the values:
\[ \lambda_{water} = \frac{589 , \text{nm}}{1.33} \]
Calculating this gives:
\[ \lambda_{water} \approx \frac{589 , \text{nm}}{1.33} \approx 442.11 , \text{nm} \]
So, the wavelength of the light in water is approximately 442 nm.
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