What is the Wavelength of a Helium-Neon Laser Beam in an Unknown Liquid?

[frederickcan]

Homework Statement

A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

Homework Equations

n=c/v
d=rt

The Attempt at a Solution

So, I'm having difficulty understanding how to calculate what the wavelength of the laser beam in the liquid is. In my attempt I tried using the index of refraction equation to determine the speed of light in the material (unknown liquid). Since, the question provided a time and distance I thought using the distance formula to find the speed would help too.

First, I converted the 30 cm to m, which gave me 0.3m.
Second, I plugged the given values into the distance formula. 0.3m= r(1.38ns) => 0.21739..
Third, I plugged the values into the index of refraction equation... n=3.0x10^8/0.21739
Now, I'm stuck. I'm not sure how to figure out the second wavelength. Do I incorporate the 633nm somehow?

(Any help would be immensely appreciated.)

 

[turin]

If you're going to rely on units, then you need to use units everywhere, not just somewhere. What is 0.21739? What are the units?

Otherwise, you're on the right track. You need to answer this question: how much does the frequency of the light in the liquid differ from the freqency of the light in air. Then, use the wave relationship: fλ=v.

 

[frederickcan]

Wait a minute you're right, I made a unit error.

If I convert the ns to s, and then proceed with the process it should make a difference in my answer.

So, if 0.3m/1.38s = 0.21739m/s <= that would be my speed of light in the material.
Then, I could figure out the frequency using the wavelength relationship. f=633 x 10^-9/0.21739m/s
Lastly, I could figure out the wavelength.
I think I may get this afterall.(Thank you for your help!)

 

[turin]

You still have a unit error. Check again how much time the light takes to travel through the liquid.

 

[Redbelly98]

If I convert the ns to s, and then proceed ...

Good idea. Try doing that conversion again.

 

[ideasrule]

Remember that the frequency of light doesn't change when the light enters a different medium. Since v=fλ and v=c/n, what must λ be?