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

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

Please post a genuine proof that frequency is conserved during refraction?

'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'

I'm not crazy, my mother had me tested.

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

Frequency is determined by the distance between wave maxima (or minima). Since you cannot get energy from nothing (nor lose it) the maxima (and minima) after passing through the boundary must be conserved, so the frequency must be constant.

Bob

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

Frequency is determined by the distance between wave maxima (or minima).

That is wavelength

'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'

I'm not crazy, my mother had me tested.

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

It's both; as they're related by the speed of light in the medium.

Bob

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

I'm kind of confused.

'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'

I'm not crazy, my mother had me tested.

Offline

Since you cannot get energy from nothing (nor lose it) the maxima (and minima) after passing through the boundary must be conserved, so the frequency must be constant.

Why does wavelength change then?

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

I'm not crazy, my mother had me tested.

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

I'm working on a diagram, It will take a while.

Bob

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

Hmm, thanks for your efforts.

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

I'm not crazy, my mother had me tested.

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

OK, I've got one. Hope it helps.

The ladder on the left represents a beam of light moving from left to right towards the boundary, shown in red.

The wavelength is represented by AB. Each cross line represents a transverse wave maximum. They are equally spaced and connected by the formula

When the beam reaches the boundary, the speed of light is lower (let's say). But the rate at which wave-fronts arrive at the boundary is unchanged. Maxima must start at the boundary at the same rate and travel through this new medium at the slower rate, let's say d < c. n is unaffected by the transmission through the boundary. CD is the new wavelength; I'll call it mu.

Bob

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

Oh yes; forgot this:

The wave-fronts are perpendicular to the direction of the beam because it is a transverse wave. As CD is shorter than AB, the beam bends towards

the normal. You can work out the usual angle of incidence and refraction connection by doing some trig. using the red line as the hypotenuse.

Bob

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

Offline

Will check tomorrow; Going to sleep

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

I'm not crazy, my mother had me tested.

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

Sleep well.

Bob

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

Offline

**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Light is an electromagnetic wave and as such it must obey Maxwell's equations. Two of Maxwell's equations (Gauss' law & Faraday's law) each impose a separate condition on the Electric Displacement Field & Electric Field respectively. Firstly, according to Gauss' law the boundary between two dielectric media (air & water) is uncharged then the normal component of the Electric Displacement Field must be continuous. Secondly, according to Faraday's law the normal component of the electric field must be continuous across the boundary of two dielectric media. The only way to satisfy both conditions is if the frequency of the light remains constant.

Offline

Pages: **1**