Hi guys, my name's Richard, I'm 16 and I have a question about Snell's Law.

(Btw, I do have a test about this in a few weeks it's just that I was sick, so I couldn't catch up in time with my class mates - more over, I'm not just asking because it's for school work, I honestly like physics :) )

Right so, I googled Snell's law and I got loads of results - definitions which include terms like : ray incident, angle of incidence, index of refraction, medium etc.

I have no idea what they are talking about and what these terms mean exactly. If someone could please just explain this stuff, the terms and Snell's Law, to me in a more or less simple way, I'd really appreciate it.

Thanks,

-XM8

The speed of light is maximum in vacuum. In vacuum, the speed is 3 * 10^8 m/s. To be accurate, it is 299,792,458 m/s, which is very close to 3 * 10^8 m/s. In other media (e.g. glass, water etc.), the speed of light is less than this. For every medium in which light can travel, there is a property called refractive index (also called index of refraction).

Refractive index of a medium = speed of light in vacuum/speed of light in that medium

The refractive index of air is very close to 1, which means that speed of light in air is very close to speed of light in vacuum. Therefore, sometimes in practice, we use the formula

Refractive index of a medium = speed of light in air/speed of light in that medium

We can also define refractive index of one medium with respect to another.

Refractive index of a medium (call it target medium) with respect to medium (call it reference medium) = speed of light in medium reference medium/speed of light in target medium

Now consider two media. Call them medium 1 and medium 2.
Make a perpendicular to the plane which separates the two media. This perpendicular is called the normal.

Suppose a light ray is moving from medium 1 into medium 2. When the ray is in medium 1, it is called incident ray. When it is in medium 2, then it is called refracted ray.
The angle between incident ray and normal is called angle of incidence.
The angle between refracted ray and normal is called angle of refraction.
Let I = angle of incidence,
r = angle of refraction

According to Snell's law ,
sin I/sin r = refractive index of medium 2 with respect to medium 1
We can also say
sin I/sin r = refractive index of medium 2/refractive index of medium 1
Note that when we simply say refractive index of a medium without saying with respect to what, it means with respect to vacuum.

The medium which has higher refractive index is called optically denser and the medium which has smaller refractive index is called optically rarer.

When light ray goes from rarer to denser medium, then
medium 1 has lower refractive index than medium 2.
Therefore, from Snell's law,
sin I/sin r > 1
Or I > r
Or r < I
This means that when light goes from rarer to denser medium, then it bends towards the normal.

When light ray goes from denser to rarer medium, then
medium 1 has larger refractive index than medium 2.
Therefore, from Snell's law,
sin I/sin r < 1
Or I < r
Or r > I
This means that when light goes from denser to rarer medium, then it bends away from the normal. When it bends away from the normal, then it may bend so much that it comes back into medium 1. This means there is no refraction but reflection. This is called as total internal reflection.
Mathematically minimum value of r for which total internal reflection occurs = 90 deg.
Value of I for which r = 90 deg is called critical angle. Let us call critical angle as C.
In Snell's law, put I=C and r=90 deg
sin C/sin 90 deg = refractive index of medium 2/refractive index of medium 1
But sin 90 deg = 1
Therefore
sin C = refractive index of medium 2/refractive index of medium 1
When I=C, then after hitting the boundary between the media, the ray grazes the boundary. When I>C, then the ray is reflected back into the first medium (i.e. total internal reflection).

As discussed above, for total internal reflection, following two conditions are needed:-
1. Light ray should move from optically denser to optically rarer medium.
2. Angle of incidence should be greater than critical angle.

Incident ray = your ray going in before being refracted
Medium = the material that the light is travelling through
Interface = the line where the light goes from one medium to another
Normal = the imaginary line at 90 degrees to the interface
Angle of incidence = the angle between the incident ray and the normal
Refracted ray = the ray after it has passed through the interface
angle of refraction = the angle between the refracted ray and the normal
Refractive index = a property of a medium, denoted by n, which relates how fast light moves through the medium. A vacuum has n = 1, other materials have n greater than 1. n = 2 means that light moves through the medium at half the speed that it moves through a vacuum.

Snells law simply states that n_1sin(\theta_i) = n_2sin(\theta_r), or perhaps easier to understandable as \frac{sin(\theta_i)}{sin(\theta_r)} = \frac{n_2}{n_1}.
Maybe even better might be sin(\theta_r) = \frac{n_1}{n_2}sin(\theta_i)

That is, the sin of the angle that the beam is refracted by, is determined by the ratio of the refractive indices, multiplied by the sin of the angle of the incoming beam.

Some of this stuff is tricky to get your head around. There's a lot of new lingo that comes along with this piece of physics.

If you have any questions please ask.

Thanks to both of you for your answers. I think I've understood the meaning of all the terms. I made a simple diagram with paint, just to see if I've understood.

http://boxstr.com/files/4487121_ssmpa/Snell%5C%27s%20Law.png

I just wasn't sure about if the interface is on the medium. Let's say the medium is water (like in the diagram) does that mean that the "line" of water, is itself the interface as well?


As for the equation, I don't really understand it fully. What I think I understand is:

The sine of the angle of refraction (i.e. 60 degrees) equals n1 / n2 multiplied by the sine of the angle of incidence (i.e. 30 degrees)

I doubt it's right but..

https://www.askmehelpdesk.com/cgi-bin/mimetex.cgi?sin(\theta_r) = \frac{n_1}{n_2}sin(\theta_i)

By the way, just to clarify some things ; The weird 0 with the letter "r" next to it, that means the angle of refraction right?
And the weird 0 with the letter "i" is the angle of incidence?

Moreover, I'm not so sure about n1 and n2. Basically the value of n1 is the speed of light is at it's maximum speed ( in a vacuum for instance) right?
And n2 means that it is at half the speed of light in a vacuum?

Another thing I don't understand is n, what is n ?


Sorry to be such a pain in the neck, this stuff is really new to me.

The interface is just the line between the 2 mediums.
For example you might have a beam going from air into water, air would be the first medium with refractive index n1, and water is your second medium with refractive index n2, the interface is the surface of the water. Likewise you might have it going from air to glass or glass to water or anything, the interface is the line (or the plane) separating the 2 mediums. The important thing to get right is that your beam is incident in the medium with n1 and refracted into the medium with n2.

\theta is a greek letter, called "theta" (thee-tah), we often use it to denote an angle of some kind. We also commonly use \phi, "phi" (fi) for angles too.

The subscript r and i are just put there to denothe the incident angle and the refracted angle. Your textbook or teacher might use a subscript 1 and 2 to match up with n1 and n2 (when the beam is in the medium of index n1, it hits the interface with angle theta1, etc).

n is kind of the reciprocal of speed. In a vacuum it's 1, in air it's very close to 1, something like 1.002. In glass it's something like 1.5 meaning that light travels 1.5 times more slowly in glass. In silicon it's 4, meaning that light travels 4 times more slowly in silicon than in a vacuum.

so n1 is simply the value for the refractive index in the first material, and n2 is it in the second material. Quoting visharad: "Refractive index of a medium = speed of light in vacuum/speed of light in that medium"

Capuchin, thanks for your reply and being so patient with me!

So first off, in each kind of situation when you study Snell's Law, you have 2 mediums - in the diagram I drew they would be air and water. The ray of incidence and the refractive index n1 are in the 1st medium (air) - and the ray of refraction, along with the refractive index n2 would be in the second medium (water).

That's correct, I hope :)

And just to clear aside the matter of the interface ; the interface is the "boundary" between the two mediums, so to speak that would be the blue line in my diagram, right? Since it does separate the air from the water.. So I assume that my assumption is correct (regardless of how ridiculous that may sound).

I think I now understand the lesson in general, but could you just do me one favour and give me an example of an equation using the same form as https://www.askmehelpdesk.com/cgi-bin/mimetex.cgi?n_1sin(\theta_i) = n_2sin(\theta_r)

I think an example might help me understand it better.

Thanks a lot for your help,

-XM8

XM8,
I cannot see the diagram. Please check the link. But, from your explanation, I can say that your understanding is correct.

You asked for an example. Consider the following:-
A light ray goes from air to glass(n=1.5). It is incident at the interface between the media at angle 30 deg to the normal. What angle will the refracted ray make with the normal?

Air's refractive index is often very close to 1. So, if it is not given, then for solving problems, we can assume it to be 1.
n1 = 1
n2 = 1.5
thetai = 30 deg
thetar = ?

n1 * sin(thetai) = n2 * sin(thetar)
1 * sin(30 deg) = 1.5 * sin(thetar)
0.5 = 1.5 * sin(thetar)
sin(thetar) = 0.5/1.5 = 1/3
thetar = sin-1(1/3) = 19.5 deg
As you can see, thetar < thetai
This means that on entering glass, the light ray bends towards the normal.

Ah OK I see :)

I think I understand it now. Thanks a lot to all of you for your help! Much appreciated :)

Just one small question - thetai and thetar ? I imagine the suffixes "ai" and "ar" were angle of incidence and angle of refraction, and that the prefix "thet" is from the greek letter "theta" ?

I'm not so sure if at my school we use that kind of way to write the equation, but regardless of if we do, if I use the above example it must be correct because it's a global way to do an equation in Snell's Law, right?


Thanks a bunch,

-XM8

the symbol \theta "theta" denotes an angle, the i or r denotes refracted or incident. I assume that visharad isn't familiar with how to use tex (the formula typesetting toolset) on our site :). You will almost universally see the symbol used, the word is just used for ease on computers sometimes.

Your school or syllabus could call the angle anything, a_i and a_r might be used, it's just a way of naming a variable, and \theta is just almost always used for an unknown angle, that's all

All right I see, but the small "i" means incident and the small "r" refracted, right? Otherwise I get everything.

Thanks for all your help!

Sorry for causing the confusion. But Capuchin has explained. Yes the suffix I means "incident" and r means "refracted".

All right. Well thanks a lot to both of you, you've helped me imensly, I really appreciate it. Thanks a lot!

:)

Cheers,

-XM8

Yes.

Any time :).

Your syllabus might use 1 and 2 instead of I and r (to denote the rays in medium 1 and medium 2), I don't know. There are no "standard" notations for this kind of thing, people just use what they think makes it most clear.