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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'

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**eigenguy****Member**- Registered: 2014-03-18
- Posts: 78

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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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,059

what does unity mean here?

friendship is tan 90°.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 97,269

It means 1.

**In mathematics, you don't understand things. You just get used to them.**

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,059

oh, thanks

friendship is tan 90°.

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Unity is strength.

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,059

yes it is better

friendship is tan 90°.

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I need an answer

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,192

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)*

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Thank You

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**eigenguy****Member**- Registered: 2014-03-18
- Posts: 78

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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