# Homework Help: Argh - De Broglie and the wave equation

1. Jan 29, 2009

### B1ueguy1

This isn't a homework question, but something which has been bugging me. I can't figure it out. Maybe it's late, but it's probably a very stupid question

If light shines onto a denser medium, the light slows down in this medium right? If the light slows down, then by the wave equation, v = fλ, since f is constant, the wavelength must decrease.

So why is it that de broglie's equation λ = h/mv implies a decrease in velocity would increase the wavelength?

I'm so confused...

2. Jan 29, 2009

### qwerty2x

v is in the denominator

3. Jan 29, 2009

### B1ueguy1

eh?

de broglie: λ = h/mv
wave equation: λ = v/f

4. Jan 30, 2009

### B1ueguy1

if anyone has any insight, could someone please help me? It's sort of urgent. I'm taking an exam tomorrow and this uncertainty is really making me nervous.

5. Jan 30, 2009

### bowma166

Well... the de broglie equation is $$\lambda=\frac{h}{p}$$. I don't really think that $$p=mv$$ works for light, because photons have no mass.

I don't really know what I'm talking about though.

6. Jan 30, 2009

### americanforest

The equation $$p=mv$$ does not hold for photons (light quanta) since they have no rest mass. For a photon, its energy, $$E=h \nu$$ (Planck's constant multiplied by frequency) is equal to its momentum multiplied by the speed of light in vacuum (Generally, for relativistic motion, $$E^{2}=(pc)^{2}+(mc^{2})^{2}$$; Since m is zero in the case of the photon $$E=pc$$. In this case, de Broglie's equation becomes

$$\lambda = \frac{h}{p}=\frac{hc}{E}=\frac{hc}{h \nu}=\frac{c}{\nu} \Rightarrow \lambda \nu =c$$