# Calculations i cant understand and make me crazy

1. Nov 11, 2009

### katatonia911

hi,

im not involved into physics but i read sometimes about it and have very curious questions:

Q1-

if E=mc2 then as i know that electromagnetic waves have mass of zero

so this mean E=0xc2 which means that c2=E/0

here i get that the E=0 , and c=infinite..which i guess is impossible

so what is wrong in my understanding of the equation?

Q2-

since the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200,000 km/s; the refractive index of air is about 1.0003, so the speed of light in air is very close to c.

what is the factor that increase the refractive index??

and if we supposed that we have a material of a very high refractive index which its value ≈ 300,000,000 what will will happen to the light? will it become somthing with mass that we can see?

Q3-

i always read when people talking about light travel speed as if light is something fixed but as i know its composed of different waves with different frequencies (rainbow colors, infra-red,UV,..) ..its getting me crazy

i dont get it.when scientists put their calculations do they put these fact's in their mind?
how they deal with it?

thank you all

Last edited: Nov 11, 2009
2. Nov 11, 2009

### yuiop

Hello kat, welcome to PF :)

The m in the equation E=mc2 is in simple terms the total mass which comprises the rest mass and the kinetic mass. For a stationary particle the total mass is simply the rest mass but for a moving object there is a kinetic component. For something moving at the speed of light all the mass is kinetic mass, so m=0 does not apply to a photon.

E = mc2 = moc2/sqrt(1-v2/c2)

where mo is the rest mass. For a photon mo=0 and sqrt(1-v2/c2)=0 so E = 0/0*c2 which is not the same as zero or infinite but is indeterminate. All that means is that the answer for this situation can not be calculated using this method. The equation that can be used for a photon (or any particle) is:

E = sqrt(mo2c4 + p2c2)

where p is the relatistic momentum of the particle. For a particle with rest mass, the relativistic momentum is equal to:

p = mov/sqrt(1-v2/c2)

and for a photon the momentum is:

p = hf

where f is the frequency of the photon and h is Planck's constant, so for a photon:

E = mc2 = sqrt(mo2c4 + p2c2) = pc

In short, the rest mass of a photon is zero, but its total mass is not and in the famous E=mc2 equation, the m does not refer just to rest mass.

The wavelength and frequency of electromagnetic waves is related according to:

c = f*w where w is the wavelength. A photon with a large frequency has a small wavelength and vice versa, but the product is always a constant speed equal to c.

Hope that helps.

Last edited: Nov 12, 2009
3. Nov 11, 2009

### Staff: Mentor

The answers for 1 and 3 given above by kev are good, so I will just do this one
The refractive index is the speed of light in vacuum divided by the speed of light in the material, and the speed of light in any material is given by
$$\frac{1}{\sqrt{\mu \epsilon}}$$
where $\mu$ is the permeability and $\epsilon$ is the permittivity of the material. The permeability of most materials is not terribly far off from that of vacuum, but dielectric materials have permittivity values that can be quite far from vacuum. That is why things like glass, plastic, diamond, and crystal all have high refractive indexes and all are good electrical insulators, the two properties are both a result of the high permittivity.

4. Nov 12, 2009

### clamtrox

Last edited by a moderator: Apr 24, 2017
5. Nov 12, 2009

### ZapperZ

Staff Emeritus
Actually, it isn't wrong, because it tells you exactly how much energy one gets when an amount of mass is converted. It is just that it isn't the whole story.

It is very similar to using F=ma. You wouldn't call that wrong, would you? Structural engineers use it all the time to build houses and buildings. Yet, it is only valid for constant "m", i.e. it is not the full story. So when you have varying m, then using that equation is not appropriate. This is exactly what is going on with the relativistic energy equation. People who haven't learned enough are using the wrong equations for the wrong situation. It is not the equation that is wrong.

Zz.

6. Nov 12, 2009

### katatonia911

Thank you all, clear answers and to the point

Last edited: Nov 12, 2009
7. Nov 12, 2009

### clamtrox

... and if 90% of the time everyone used F=ma to systems where mass wasn't constant, would you say that equation was still right? Or if structural engineers tried to build houses from photons and they'd say "these guys can't feel any forces 'cause their mass is zero".

8. Nov 12, 2009

### ZapperZ

Staff Emeritus
I'm not sure what your point is here, since you are actually supporting what I just said. It really doesn't matter how many percent of the time people use F=ma incorrectly. It is still incorrect.

E=mc^2 IS correct for what it is conveying. When you want to calculate the energy conversion from an amount of mass, what else do you use? For that specific usage, it is correct. So what are we arguing about here? I'm hoping this is not about "covariant mass" versus "rest mass" versus "relativistic mass", because that has been discussed ad nauseum.

Zz.