Calculating frequency and wavelength in solution

In summary, the problem involves a laser beam incident on a corn syrup solution at an angle of 30.0°, refracted to 22.84°. The index of refraction of the solution is found to be 1.29. Using the vacuum wavelength of 632.8 nm, the wavelength of the red light in the solution is calculated to be 490.5 nm. When trying to find the frequency in the solution, the incorrect method of using the wavelength in the solution was used. The correct method is to use the wavelength in vacuum, which results in a frequency of 4.74*10^14.
  • #1
Carrie
27
0

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!
 
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  • #2
Carrie said:
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
$$
f = \frac{c}{\lambda_0}
$$.
 
  • #3
Ohhh, I see where I went wrong now. Thank you! :smile:
 

1) How do you calculate frequency and wavelength in solution?

To calculate frequency and wavelength in solution, you will need to know the speed of light in the given solution and the refractive index of the solution. The formula for calculating frequency is f = c/n, where c is the speed of light and n is the refractive index. To calculate wavelength, you can use the formula λ = c/f.

2) What is the difference between frequency and wavelength?

Frequency and wavelength are two different properties of light. Frequency is the number of complete wavelengths that pass a point in one second, measured in Hertz (Hz). Wavelength is the distance between two consecutive peaks or troughs of a wave, measured in meters (m).

3) How does the refractive index of a solution affect the frequency and wavelength?

The refractive index of a solution is a measure of how much the speed of light is reduced when passing through that solution. As the refractive index increases, the frequency of light decreases, while the wavelength increases. This is because light travels slower in a solution with a higher refractive index, resulting in a longer wavelength.

4) Can you calculate frequency and wavelength in any type of solution?

Yes, the formula for calculating frequency and wavelength in solution applies to all types of solutions, as long as the speed of light and refractive index values are known. However, the values for these variables may vary depending on the type of solution.

5) How is the speed of light in a solution determined?

The speed of light in a solution can be determined experimentally by measuring the time it takes for light to travel through a known distance of the solution. It can also be calculated using the refractive index of the solution and the speed of light in a vacuum, using the formula c = c0/n, where c0 is the speed of light in a vacuum and n is the refractive index of the solution.

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