Optics 2) Snell`s law

Hi,
here it comes, here it goes! This is gonna be probably my first post where some real physics is involved (actually it is far too easy)! I am going to write about Snell`s law which is the law describing how light changes the angle of traveling when it enters to different medium.


First of all I have an experiment for you which goes as follows: you take a bowl which for the start will be empty except some small thing that will sink in water later on.
1) place your chin on the edge of table and move the bowl so you can see what is inside.

2) move it on the place where the edge will block your view and then place a water inside.

3) You should see the thing inside again!
This is because the light changes its angle of traveling which makes for example straw in bottle of water look so distorted (or hunter`s eye cheated when he is seeing the fish on different place then where it actually is (this makes water not look so deep as it actually is)), as that the higher part is not even connected sometimes to the lower one.
On the picture on the left you can see that the lower and upper part does not match which is because of the light which change the angle of traveling when entering glass then water then glass and air.

Fine, so what depends on how much will the angle change?
It is the difference between the speeds of light in both medium.

There is thing which is called refractive index: n. All mediums (which do let some light through) have some refractive index. Vacuum has 1, it does not change the angle of light. Air has about 1,0003 so you will usually see 1 also. But water has 1.33 and refractive index of glass ranges from 1.5 to 1.9 and the highest index known is for germanium=4.

When light enters another medium Snells law comes!

\frac{\sin\alpha_1}{\sin\alpha_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1}
Btw. if you want to know n.. n=c/v (c is speed of light and v is the speed of light in current medium)

On the left you can see the example of light ray traveling from one thing to another. So for example if you did not know the angle in which it will fly in the second medium (water now) you would do this:
alfa=50°
beta=?
n(air)=1
n(water)=1.33

sin 50°/sin beta=1.33/1
sin 50°/1.33=sin beta
0.77/1.33=sin beta
0.58=sin beta
beta=sin^-1(0.58)
beta=35.5°
This is all beta about which I am talking here would represent theta two on the picture. So if you have enough information you can either get the angles or the speeds of light in mediums or the refractive indexes.

On the gif you can see pretty neat animation of how the waves of light are slower in the water and the red line clearly represents how the light is refracted.

Dragallur

Pictures except the first one are from wikipedia pages about refractive index and Snell`s law.
If you want to check out my first post about optics click here.
1st picture source

 

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