# Can refractive index of a material be less than unity?

1. Jan 3, 2016

And what is the difference between refractive index and absolute refractive index? Why do we use relate two absolute refractive index to find the refractive index of a particular material say we need to find refractive index of water with respect to ice.and why do we always put the higher value above and lower value below while dividing to obtain a refractive index?
Got finals coming up! Hope I get perfect answers!

2. Jan 3, 2016

### cnh1995

I'm no expert, but I remember from my physics class that the absolute refractive index is defined as,
RI=
speed of light in the vacuum/ speed of light in material.
Absolute R.I.less than unity implies the speed of light in that material is greater than that in the vacuum, which is impossible. Relative RI can be less than unity. If relative RI of B w.r.t A is greater than 1, relative RI of A w.r.t B will be less than 1.

3. Jan 3, 2016

### blue_leaf77

In plasma, the refractive index can be less than one.
Honestly, I am not quite familiar with the concept of relative refractive indices. But the placement of the higher value in the numerator is just a matter of favor, IMO.

4. Jan 3, 2016

### blue_leaf77

Refractive index is defined as $n=c/v_p$ where $v_p$ is the so-called phase velocity, this is the rate at which the peaks and throughs in the wave advance. This quantity can be bigger than $c$. It is the group velocity which must not exceed $c$.

5. Jan 3, 2016

Your answer is damn perfect.Thanks a lot but why do we relate two absolute refractive indiced in order to obtain a relative refractive index? I mean why can't we relate speed of light in ice and water instead of relating the absolute refractive index of ice and water?

6. Jan 3, 2016

### cnh1995

I believe that is how relative R.I. is defined. But you can take the ratio of the speeds if you want. When you take ratio of absolute R.I.s, there is one common thing in each absolute RI and that is the speed of light in vacuum. It will cancel out and ultimately give the ratio of speeds. You can verify it mathematically.

7. Jan 3, 2016

### lychette

If light travels from medium 1 into medium 2 then the refractive index of medium 2 with respect to medium 1 is given by
1n2 = c1/c2 where c1 is the speed in medium 1 and c2 is the speed in medium2
If medium 1 is vacuum then the refractive index (of medium 2) is called the absolute refractive index. so n2 = c/c2
where c = speed of light in vacuum
suppose medium 1 is glass and medium 2 is water then gcw = refractive index of water with respect to glass.
ng = c/cg and nw = c/cw......can you see that
gnw = nw/ng ?
hope this helps

8. Jan 3, 2016

Thank you so much! Damn perfect answer!

9. Jan 3, 2016

Suppose if they ask the refractive index of water with respect to glass should I keep the speed of light in glass above and speed of light in water below while dividing in order to obtain the relative RI? Or the vice versa?
When the word "with respect " comes I become totally confused about which one to divide with what to get the relative RI.

10. Jan 3, 2016

Suppose if they ask the refractive index of water with respect to glass should I keep the speed of light in glass above and speed of light in water below while dividing in order to obtain the relative RI? Or the vice versa?
When the word "with respect " comes I become totally confused about which one to divide with what to get the relative RI.

11. Jan 3, 2016

### cnh1995

I believe lychette has nicely explained this in #7. RI of water w.r.t. glass will be
speed in glass/speed in water. If there were vacuum instead of glass in the formula, this would be the absolute RI of water.

12. Jan 3, 2016

Well,that is clear.but lychette is not clear with something else.when we say refractive index of water with respect to glass should speed of light in glass be divided with speed of light in water or the other way around?

13. Jan 3, 2016

### cnh1995

RI of medium 2 w.r.t medium 1=
Speed in medium 1/ speed in medium 2.
It's there in the 4th line in lychette's post. When you take medium 1 as vacuum, this becomes abosolute RI of medium 2.

14. Jan 3, 2016

Well my book says something else!
When refractive index of diamond with respect to glass is 1.6 and absolute refractive index of glass is 1.5 then the absolute refractive index of diamond should be 0.9,right? That is what I get when I go with your definition while my book says the answer is 2.40.I don't know how that is possible.
Try out yourself.

15. Jan 3, 2016

### blue_leaf77

Relative refractive indices may be a subjective matter, it's just a matter of preference which goes to the numerator which to the denominator. If you are that worried over this, I suggest that you follow the definition of your lecturer. If your lecturer has never talked about relative refractive indices and If the textbook you are reading is the same book your lecturer uses in his class, it may be good to follow the book's definition.

16. Jan 3, 2016

### cnh1995

Refractive index of diamond w.r.t glass
=speed in glass/speed in diamond
=absolute RI of diamond(2.4)/absolute RI of glass(1.5)
2.4/1.5=1.6=relative RI of diamond w.r.t glass..
Your book seems to be right!
If you are still having problem, try remembering it this way:
For glass and diamond,
(Absolute RI of glass)*(speed of light in glass)=
(Absolute RI of diamond)*(speed of light in diamond.)
This is true for any two media.

Last edited: Jan 3, 2016
17. Jan 3, 2016

"=speed in glass/speed in diamond
=absolute RI of diamond(2.4)/absolute RI of glass(1.5)"

You first say speed in glass/speed in diamond and then it changes to absolute refractive index in diamond/absolute RI in glass.How come you interchange the numerator and the denominator?

18. Jan 3, 2016

In my book the medium 2 with respect to medium 1 is givenas medium2/medium 1 as such while lecturer explained the way you guys say ".medium 1/medium2."
It is rather confusing about which medium should be placed where in relative refractive index but it seems clear in absolute refractive index since air or vaccum is always supposed to be in numerator.
It becomes difficult to solve problems related to relative refractive index then!

19. Jan 3, 2016

### cnh1995

Because RI of 1 w.r.t.2 =
speed of light in 2/speed of light in 1
Speed in the medium of which the RI is to be calculated comes in the denominator. You can verify.
Absolute RI of water= speed in vacuum/speed in water
Absolute RI of glass=speed in vacuum/speed in glass
Now, if you take the ratio
Abs RI of water/ Abs RI of glass,
wouldn't it be
speed in glass/speed in water? i.e. RI of water w.r.t glass?

20. Jan 3, 2016