# Wavelength of light in water

1. Dec 8, 2008

### Soojin

1. The problem statement, all variables and given/known data

"Light of wavelength 0.527 µm (in air) enters the water in a swimming pool. The speed of light in water is 0.700 times the speed in air. What is the wavelength of the light in water?"

2. Relevant equations

v = c /n, where n = 1.33 ,the index of refraction

3. The attempt at a solution

The wavelength of light in air is given. $$\lambda$$=0.527
I looked up the speed of light in air -- 299704644.54 m/s
I also know that the speed of light in water is 0.700(299704644.54)

I am not sure how to relate these numbers to v = c/n though, or the equation to use to find the $$\lambda$$ of light in water. Can anyone offer any insight? Thanks!

2. Dec 8, 2008

### Staff: Mentor

What's the relationship between speed, wavelength, and frequency for any wave? Which of those parameters remains unchanged when light travels from one medium to another?

3. Dec 8, 2008

### Soojin

frequency = v / $$\lambda$$, so I would think the frequency would be left unchanged.

So I'm thinking I could do:

f = (speed of light in air)/0.527

to solve for the frequency, then use that value to solve for the wavelength of light in water?

4. Dec 8, 2008

### Staff: Mentor

Good.

OK, but even easier is to realize that the ratio v/λ must remain fixed, so λ decreases by the same factor that the speed decreases.