# Reflection fase change

1. Apr 20, 2005

### marlon

Reflected light will experience a 180 degree phase change when it reflects from a medium of higher index of refraction and no phase change when it reflects from a medium of smaller index. This is very well known. However i am wondering why that is ? Can anyone give me some calculations that actually prove this ???

Thanks

marlon

2. Apr 20, 2005

### Meir Achuz

The "Fresnel Relations" in physics-optics give the reflected E' field as
E'=E_{incident}[(n_1-n_2)/(n_1+n_2)] for normal incidence.
This shows the phase change. The FRs are derived in most junior level EM or optics texts. They follow from the BCs on E and H at the interface of two dielectrics.
The transverse components of each are continuous.

3. Apr 20, 2005

### dextercioby

The theory of reflection of light is presented in any textbook of optics.I liked and reccomend the bible:M.Born & P.Wolf:"Principles of Optics",any edition,chapter 1,starting with page 36.

Daniel.

4. Apr 21, 2005

### marlon

Guys, if it is so easy why not give me a specific explanation as to why the phase change happens in this particular case ? Dexter, referring to books is useless because i am never gonna read that book. I am asking for an explanation and if you cannot give it then don't post just for the sake of posting....Please...

So my question still stands...Anyone who knows the answer ???

regards
marlon

5. Apr 21, 2005

### dextercioby

Marlon,the equation Meir posted states that,for normal incidence,

$$E_{reflected}=E_{incident}\frac{n_{1}-n_{2}}{n_{1}+n_{2}}$$

If $n_{1} < n_{2}$,then $E_{reflected}= - k E_{incident}$ (1)

,where $k=:\frac{n_{2}-n_{1}}{n_{1}+n_{2}}>0$ (2)

Okay.Now,u write,following (1) & (2)

$$E_{reflected}=k E_{incident}e^{i\pi}$$ (3)

Is it any clear?Guess not.I introduce the phases and the polarization vectors,okay,then

$$\vec{E}_{reflected}=\vec{e_{p}}E_{reflected}e^{i\left(\vec{k}_{reflected}\cdot\vec{r}-\omega t\right)}$$ (4)

Using (3),u see where that phase change comes from.

http://scienceworld.wolfram.com/physics/FresnelEquations.html

(For the graph).

Here's a nice course

http://www.ece.rutgers.edu/~orfanidi/ewa/

BTW,it's PHASE.

Daniel.

6. Apr 21, 2005

### marlon

thanks dexter