# Why is the speed of light said to be constant when we know it slows down in a medium? [duplicate]

If we ask someone what the speed of light is, they will say that it is constant and its value is $3\times 10^{8}\ \mathrm{m/s}$.

But if we recall refraction of light, we say that when the light travels from a rarer medium to a denser medium then it slows down.

But we still say that its speed is constant. Why?

## marked as duplicate by Bill N, John Rennie, Qmechanic♦Jan 4 '17 at 18:19

• Possible duplicate of physics.stackexchange.com/q/466, or physics.stackexchange.com/q/165855 and links therein. – Bill N Jan 4 '17 at 16:14
• Note to add to the answers: we often say "the speed of light is constant" rather than "the speed of light in a vacuum is constant" out of linguistic laziness. Everybody quickly learns this little fact, and its so profound that it gets rooted in our mind quickly. We don't need those extra words. Unfortunately for those learning the topic, such as yourself, we do need to do a better job of being precise with our words during the process of teaching someone. – Cort Ammon Jan 4 '17 at 17:19

The speed of light in vacuum is said to be constant. In a medium, the speed depends on the density of the material, and even on the direction of propagation.

• @Physicist most people omit the "in vacuum" for simplicity, but when books try to make a precise statement, they always include that phrase. – AccidentalFourierTransform Jan 4 '17 at 17:27

The speed of light in vacuum is $3 \times 10^8 \,\mathrm{m/s}$ and that is a universal constant. Apart from that, the speed of light in a definite and particular optical medium always varies ( In some cases, during birefringence, the speed of light changes inside a medium depending upon direction of propagation) with small changes in the magnitude depending on the pressure, temperature and a few other physical factors.

• There's a big difference. If the light has further to travel then that would be why it takes longer to move through the median and not because the speed slowed down. – Bill Alsept Jan 4 '17 at 16:33
• What happened to all the other comment? – Bill Alsept Jan 4 '17 at 16:41
• @BillAlsept I dont know they all vanished, all on a sudden. – SchrodingersCat Jan 4 '17 at 16:41
• I don't think your second sentence is true. In any particular optical medium the refractive index is affected by all sorts of things e.g. temperature and pressure. – John Rennie Jan 4 '17 at 17:34
• @JohnRennie Yes, thanks for informing me. I have added it to my answer but I checked that the error due to this dependence is small. You can check the paper that I have linked in my answer. – SchrodingersCat Jan 4 '17 at 17:45

Light is a disturbance of the EM field that propagates at a constant speed. As others have said the speed of light is constant in a vacuum. In other media it's speed will appear to vary because it does not take the same direct path as it would've in a vacuum.

Why the speed of light is said to be constant?

Because of the tautology wherein we use the motion of light to define the second and the metre, then use them to say what the speed of light is. See http://arxiv.org/abs/0705.4507 :

"Following Ellis 1, let us first consider c as the speed of the photon. Can c vary? Could such a variation be measured? As correctly pointed out by Ellis, within the current protocol for measuring time and space the answer is no. The unit of time is defined by an oscillating system or the frequency of an atomic transition, and the unit of space is defined in terms of the distance travelled by light in the unit of time. We therefore have a situation akin to saying that the speed of light is “one light-year per year”, i.e. its constancy has become a tautology or a definition".

The speed of light in vacuo is not constant. See Einstein saying so here.

If we ask someone what is the speed of light, then everyone will say that it is constant and its value is $3\times 10^{8}m/s$.

Not me. I'll say it isn't constant, and that 299,792,458 m/s at one elevation is not the same as 299,792,458 m/s at another because the seconds are different.

But if we recall our mind about refraction of light. we says that when the light travel from a rarer medium to a denser medium then its speed become slow. See the Image first. But still its speed is constant. WHY ???

Because it isn't going straight any more. The light is going at the same speed in the glass as in the air at that location, or in vacuum at that location. It's still travelling at c, but it isn't propagating in a straight line. Instead it's bending back and forth as it passes the atoms. For an analogy, imagine you can walk along a pavement at 4mph. When the pavement is empty, it takes you an hour to travel four miles. But when the pavement is crowded, you're dodging around people. You're still walking at 4mph, but it takes you an hour and a half to travel the four miles. Note too that if you're a little old lady with short little steps walking at 4mph, you're held up more than if you're a big guy with long strides walking at 4mph. In similar vein short-wavelength blue light is held up more than long-wavelength red light. So it refracts more. The effective speed or phase velocity is less. But both the blue and red light are still propagating at c.

• John, I agree with your answer about The light bending back-and-forth between the atoms and thus taking a longer path. I posted that earlier but someone erased my previous comments. I'm not sure why? – Bill Alsept Jan 4 '17 at 18:00
• @Bill Alsept : I don't know Bill. Perhaps you should ask in the chatroom? – John Duffield Jan 5 '17 at 13:15
• We do not use the motion of light to define the second, and this answer fails to distinguish between the local speed of light and the coordinate speed of distant light. The former is constant, the latter is not, see also e.g. this answer. – ACuriousMind Jan 6 '17 at 15:16
• @ACuriousMind : we do use the motion of light to define the second. It's "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom". You effectively sit there counting microwaves going by, and when you get to nine billion, you jump up and say that's a second. The answer you refer to demonstrates a lack of understanding of the tautology pointed out by Magueijo and Moffat. If you doubt me on this ask a question and I'll answer it in detail. – John Duffield Jan 6 '17 at 16:21

Speed of light is a constant. That is $3\times10^8$ m/s.

Now the question is why it is thought to be a fundamental constant.

Let's say there is a ball moving with 3 m/s speed and you are moving towards ball with speed 2 m/s, what is the relative velocity of ball for you , that is 5 m/s.

Now apply same logic for light. Light is coming towards you with speed c and you are moving towards light source with velocity v what is the speed of light relative to you c+v? No! That will remain c.

Several times the experiments were performed (look for Michaelson Morley experiment) to check this result but it was found that the light speed do not change with the relative speed of observer with respect to the light source.

Due to this reason the speed of light in vacuum is taken as constant.

• I'm not sure if that is true. They say Andromeda galaxy is blueshifted because we are moving toward it. – Bill Alsept Jan 4 '17 at 18:26
• @BillAlsept Blue shift due to Doppler effect changes frequency not the velocity of light. – hsinghal Jan 4 '17 at 18:28
• How you perceive frequency is directly related to velocity and time – Bill Alsept Jan 4 '17 at 19:03
• Frequency x wavelength = speed of wave. Frequency increases, wavelength decreases speed of light remains constant. – hsinghal Jan 4 '17 at 19:08
• Exactly, so if the speed is not constant you will get blue or red shift. Speed of light stays constant but the rate of change speeds up or slows down depending – Bill Alsept Jan 4 '17 at 19:14