Relationship between wavelength and frequency in a medium

[KaseyKC]

Homework Statement

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.[/B]

Homework Equations

wavelength x linear frequency = speed of light
speed of light = refractive index x speed of light through the material

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.

 

[andrevdh]

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

 

[KaseyKC]

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

It says I need the relationship between them though.

 

[DeldotB]

Well,

first off: Higher Frequency = Lower wavelength

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

 

[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.

 

[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" .

 

[andrewkirk]

the speed in the medium
would be n x c not "refractive index x speed of light through the material" .

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

Refractive Index