Homework Help: Relationship between wavelength and frequency in a medium

1. Jul 18, 2015

KaseyKC

1. The problem statement, all variables and given/known data
Write down the relationship between the linear frequency and the wavelength of a light wave when the wave is propagating in a medium of refractive index, n.

2. Relevant equations
wavelength x linear frequency = speed of light
speed of light = refractive index x speed of light through the material

3. The attempt at a solution
Rearranging the above equations results in an answer of wavelength x linear frequency = refractive index x speed of light through the material.

2. Jul 18, 2015

andrevdh

Both the speed and the wavelength changes in the medium.
The frequency stays the same though.

3. Jul 18, 2015

KaseyKC

It says I need the relationship between them though.

4. Jul 18, 2015

DeldotB

Well,

first off: Higher Frequency = Lower wavelength

n=c/v where v=(wavelength)(frequency)

Last edited: Jul 18, 2015
5. Jul 19, 2015

andrewkirk

Do you know the relationship between wavelength, frequency and speed of propagation of a wave (any wave)? Hint: it's a very simple formula involving only those three numbers, an equals sign and a multiplication.

Now to answer this specific question, just write the same formula, and for speed of propagation, use 'speed of light through the material', as given by making that the subject of the second formula you gave above. You'll end up with an equation involving wavelength, frequency, c and refractive index.

6. Jul 20, 2015

andrevdh

wavelength x linear frequency = refractive index x speed of light through the material
yes, but the wavelength would be diffferent in the medium and the speed in the medium
would be n x c not "refractive index x speed of light through the material" .

7. Jul 20, 2015

andrewkirk

I believe it's the other way round: speed in medium (v) = c/n, not n x c.

Refractive Index