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

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,031

what does unity mean here?

friendship is tan 90°.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

It means 1.

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,031

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,031

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,647

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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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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