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#1 2014-03-21 05:28:28

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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REfraction Exercise

i3MjLid.jpg

Will the refractive index of B relative to C be more than unity or less than unity?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2014-03-21 11:46:23

eigenguy
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Registered: 2014-03-18
Posts: 78

Re: REfraction Exercise

Snell's Law

,
where n is the index of refraction of the medium, and θ is angle of incidence to the normal (the angles shown).

Assume (1) is the air and (2) is the medium, then the left side of the equation for Medium B and Medium C is the same. Hence:


Since sine is increasing and 45 > 40, the index for B must be smaller than the index for C.


"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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#3 2014-03-21 12:43:06

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,202
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Re: REfraction Exercise

So is the refractive index of B relative to C be more than unity or less than unity?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2014-03-23 16:19:02

niharika_kumar
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From: Numeraland
Registered: 2013-02-12
Posts: 894

Re: REfraction Exercise

what does unity mean here?


friendship is tan 90°.

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#5 2014-03-23 18:44:56

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: REfraction Exercise

It means 1.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#6 2014-03-23 19:28:37

niharika_kumar
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From: Numeraland
Registered: 2013-02-12
Posts: 894

Re: REfraction Exercise

oh, thanks


friendship is tan 90°.

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#7 2014-03-23 21:45:37

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,202
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Re: REfraction Exercise

Unity is strength. tongue


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#8 2014-03-23 21:59:29

niharika_kumar
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From: Numeraland
Registered: 2013-02-12
Posts: 894

Re: REfraction Exercise

yes it is better tongue


friendship is tan 90°.

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#9 2014-03-23 22:12:28

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,202
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Re: REfraction Exercise

I need an answer sad


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#10 2014-03-23 23:26:55

bob bundy
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Registered: 2010-06-20
Posts: 6,268

Re: REfraction Exercise

hi Agnishom,

refractive index of B relative to C

If I have understood correctly, your problem is to understand what is meant here by relative.

According to

http://physicsnet.co.uk/a-level-physics … efraction/

The relative refractive index can more or less than 1. If we go from material 1 with refractive index (n1) into material 2 with refractive index (n2). Then we can find the relative refractive index 1n2 by dividing the speed of light in material 1 (c1) by the speed of light in material 2 (c2) OR by dividing the refractive index of material 2 (n2) by the refractive index of material 1 (n1) OR by dividing the sine of the incident angle (q1) by the sine of the refracted angle (q2). - See more at: http://physicsnet.co.uk/a-level-physics-as-a2/waves/refraction/#sthash.4cWHfaBb.dpuf

In your example using n for air, na for A, nb for B and nc for C, you know

What you want is

As sine is increasing in the range 0 - 90, this means that the answer is less than 1.

Take care with the way a question is worded because index C relative to B would be the reciprocal of the previous.

Think of RI as a measure of how much the light is bent as it passes between the media.  C bends light more than B.  The index of B relative to C means the light is passing from C into B, so the beam of light 'straightens out' or bends less.


Bob

Last edited by bob bundy (2014-03-23 23:37:30)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#11 2014-03-24 00:42:32

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,202
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Re: REfraction Exercise

Thank You big_smile


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#12 2014-03-26 00:38:10

eigenguy
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Registered: 2014-03-18
Posts: 78

Re: REfraction Exercise

Agnishom wrote:

So is the refractive index of B relative to C be more than unity or less than unity?

eigenguy wrote:

Since sine is increasing and 45 > 40, the index for B must be smaller than the index for C.

When smaller numbers are divided by larger numbers, the ratio is < 1.

Bob has gone into greater detail, but I had already provided the answer.


"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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