Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,754
Website

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

Offline

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

eigenguy
Member
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

Offline

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,754
Website

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

Offline

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

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

Re: REfraction Exercise

what does unity mean here?


friendship is tan 90°.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,628

Re: REfraction Exercise

It means 1.


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

If it ain't broke, fix it until it is.

Offline

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

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

Re: REfraction Exercise

oh, thanks


friendship is tan 90°.

Offline

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,754
Website

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

Offline

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

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,056

Re: REfraction Exercise

yes it is better tongue


friendship is tan 90°.

Offline

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,754
Website

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

Offline

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,066

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)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,754
Website

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

Offline

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

eigenguy
Member
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

Offline

Board footer

Powered by FluxBB