# Refractive index

My textbook says it has been proven that the refractive index of a medium is a ratio between the speed of light in air or vacuum and the speed of light in a medium. It says that the ratio is the same as sini/ sinr . But isnt't it the inverse? And, can someone please explain this law to me
In simple terms ?

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Simon Bridge
Homework Helper
You mean Snell's Law? ... that is easiest to understand (without quantum mechanics) in terms of the something more concrete ...

imagine a lifeguard sees a swimmer in trouble - it is important that he gets to the swimmer in the shortest possible time.

He could run a distance d to the water, then run along the shoreline a distance s, then dive in and swim a distance c out to the swimmer. But that would not be the quickest way.

If he runs across the sand at v and swims at a lesser speed u ... what is the best path for him to take?

Go work it out - at the end of which, you will understand Snell's law.
Light always takes the path of least time.

Angles of incidence and refraction can be confusing....it depends on which way the light is travelling.
I would write the relationship as
Speed in air/ speed in medium = sine of angle in air/ sine of angle in medium
This also means that it = wavelength in air/ wavelength in medium

Thanks I understand now , but what about the sini/sinr law ?

the sinei/siner law is just another way to state that light (any wave) changes speed as it passes from one medium into another.
The ratio speed in air(vacuum) / speed in medium is a constant known as the refractive index of the medium with respect to air. This is also the ratio sinei/siner
It is given the symbol n
In general speed in medium 1/ speed in medium 2 = sine angle in 1/sine angle in 2 and is known as the refractive index of medium 2 with respect to medium 1
This is Snell's law.

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Uh Simon bridge, I don't get you .
Er I think that you all think that I don't know snell's law. Actually I know and understand why it is like that , but I was referring more to the visualisation in
My question. As in , the relationship between the incident angle and the refracted angle is related to the refractive index of both mediums right ? So if the light ray travels from air to glass, the ray will be refracted towards the
Normal but how much it is refracted depends on the difference in refractive index in both mediums right ? So my question is how exactly are the angles related to the refractive index in terms of visuals? To put it
More simply, how do you derive snell's law ?

Oh and technician, thanks for the explanation, but actually my reply was meant forzhermes. I didn't see the next two replies at that time .thanks anw!

Simon Bridge
Homework Helper
Normal but how much it is refracted depends on the difference in refractive index in both mediums right ? So my question is how exactly are the angles related to the refractive index in terms of visuals? To put it
More simply, how do you derive snell's law ?
The reply I gave you is the method for deriving Snell's law.
Did you try it?

Put the lifeguard at position (0,d) and the swimmer at (s,-c) - the lifeguard has to enter the water at a position x: 0<x<s ... find position x that minimizes the time to reach the swimmer. (Relate it to the normal angles to the shoreline to get Snell's Law.)

If the lifeguard has some high speed w under ideal conditions - say on a track - then we can define a "refractive index" for the sand and the water by nsand=w/v and nwater=w/u.

Snell's law is not restricted to light. Give it a go.

Simon Bridge
Homework Helper
[edited out the spambot, thanks Cthugha]
The optical refractive index of a single material is defined as the ratio of the speed of light in a vacuum with the speed of light in the material.

But refraction is a wave property - water-waves for example, moving from deep (fast) water to shallow (slow) water turn towards the normal ... which is why waves always come directly in towards the beach.

Refraction is not just a wave property. The lifeguard in the example above also has to change his path when he enters the water - turning towards the normal - to get to the swimmer soonest. It is possible to give the beach and the water an analogous index which will be a constant for a given lifeguard at a particular time in his career.

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Cthugha
Brady43Willia is a kind of spambot that screens forums and writes answers that represent the first answer found in google or some other database when the thread title is entered. At the bottom of every post a little advertisement link to some shop is attached. I reported that post.

I have seen this kind of bot in several other forums and it is very creepy how "low profile" spambots have become nowadays.

Simon Bridge
Homework Helper
Thanks Cthugha - I should have been more alert.
The link even looked like it belonged...

Once the lifeguard problem is completed, it leaves only the thorny question of how the light knows to obey Snell's Law :) (how does the photon know that is the path of least time?) but I'll wait to be asked.

Ok, So I get why light bends, and that it takes the path of Least time, but how does this explain how the relationship between the angle of incidence and the angle f refraction is related to the change in speed of light in diff mediums?

Claude Bile