# How does Band Gap and Refractive index relate to Wavelength?

1. Nov 9, 2015

### Nyfinscyf

1. The problem statement, all variables and given/known data
Nobel prize for physics for blue laser diode using Gallium Nitride with band gap of 3.4 eV and a refractive index of 2.429.
Explain how these parameters determine at what wavelength a Gallium Nitride semiconductor will laser at.

2. Relevant equations
$E=\frac{hc}{\lambda}$
Blue wavelength $\approx 445 nm$

3. The attempt at a solution
This equation will give the energy band gap wavelength. But how does the refractive index factor into this? I know it changes the velocity that the light moves through the medium.
But I'm still not sure how to answer the question.

Last edited by a moderator: May 7, 2017
2. Nov 10, 2015

### Simon Bridge

When light goes from one medium to another, it's wavelength changes.

3. Nov 10, 2015

### Nyfinscyf

Using the equations I can get:
$E=\frac{hc}{\lambda}$
$\lambda=\frac{hc}{E}=\frac{1240~eV~nm}{3.4~eV} \approx 365~nm$
The velocity of the light changes in the medium by $v=\frac{c}{n}$ replacing c in the above by the velocity in the medium gives
$\lambda=\frac{hv}{E}=\frac{hc}{nE}=\frac{1240~eV~nm}{(2.429)(3.4)~eV} \approx 150~nm$

I don't see how this gives blue light of 445 nm.