Calculating frequency and wavelength in solution

[Carrie]

Homework Statement

A laser beam is incident at an angle of 30.0° from the vertical onto a solution of corn syrup in water. The beam is refracted to 22.84° from the vertical.

(a) What is the index of refraction of the corn syrup solution?
I already got the answer of 1.29.
(b) Assume that the light is red, with vacuum wavelength 632.8 nm. Find its wavelength in the solution.
I already got the answer of 490.5 nm.
(c) Find its frequency in the solution?
?

Homework Equations

n1sin(theta)1 = n2sin(theta)2

frequency = c/wavelength

The Attempt at a Solution

I already know the answer, but I'm just confused as to why.

It's asking for the frequency in the solution, so I used f=3*10^8/490*10^-9, which got me 6.1*10^14.

However, this is wrong, and the correct answer did it like this and used f=3*10^8/632.8*10^-9, which gets you the answer of 4.74*10^14. I'm confused because if you're trying to find the frequency in the solution, why are you using the wavelength in the vacuum? Why not use the wavelength in the solution?

Thank you!

 

[blue_leaf77]

why are you using the wavelength in the vacuum? Why not use the wavelength in the solution?

If $v$ and $\lambda$ is the light velocity and wavelength in a medium then $v=c/n$ and $\lambda = \lambda_0/n$. Then
$$
v = \lambda f \\
\frac{c}{n} = \frac{\lambda_0}{n} f
$$
hence
$$
f = \frac{c}{\lambda_0}
$$.

 

[Carrie]

Ohhh, I see where I went wrong now. Thank you!