Can refractive index of a material be less than unity?

[Anithadhruvbud]

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!

 

[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.

 

[blue_leaf77]

And what is the difference between refractive index and absolute refractive index?

In plasma, the refractive index can be less than one.

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?

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.

 

[blue_leaf77]

Absolute R.I.less than unity implies the speed of light in that material is greater than that in the vacuum,

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 $c$.

 

[Anithadhruvbud]

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.

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?

 

[cnh1995]

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?

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.

 

[lychette]

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!

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 _gc_w = refractive index of water with respect to glass.
n_g = c/c_g and n_w = c/c_w...can you see that
_gn_w = n_w/n_g ?
hope this helps

 

[Anithadhruvbud]

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.

Thank you so much! Damn perfect answer!

 

[Anithadhruvbud]

But there is this one question that breaks my head when I read your answer.
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.
If that is answered properly,I think I can be more clear about this topic.[/QUOTE]

 

[Anithadhruvbud]

But there is this one question that breaks my head when I read your answer.
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.
If that is answered properly,I think I can be more clear about this topic.[/QUOTE][/QUOTE]

Thank you so much! Damn perfect answer!

 

[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.

 

[Anithadhruvbud]

I believe lychette has nicely explained #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.

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?

 

[cnh1995]

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?

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.

 

[Anithadhruvbud]

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.

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.

 

[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.

 

[cnh1995]

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.

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.
Good luck for your finals!

 

[Anithadhruvbud]

"=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?

 

[Anithadhruvbud]

Relative refractive indices may be a stive 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.

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 vacuum is always supposed to be in numerator.
It becomes difficult to solve problems related to relative refractive index then!

 

[cnh1995]

[QUOT95, post: 5333972, member: 552336"]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.
Good luck for your finals![/QUOTE
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?

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?

 

[Anithadhruvbud]

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?

Oops! How did I forget that! Looks like am going to rock my finals!
Thanks a lot!

 

[lychette]

Oops! How did I forget that! Looks like am going to rock my finals!
Thanks a lot!

You may find the notation ₁n₂ = c₁/c₂ useful.
It means light going FROM 1 into 2. So _wn_g = c_w/c_g which neans light going FROM water into glass. It is called 'the refractive index of glass with respect to water"
Can you see that _gn_w = c_g/c_w means the "refractive index of water with respect to glass ? and = 1/_wn_g.
the term "with respect to..." can cause confusion !