Refractive index in dispersion?

[Kaydubz]

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This has been bugging me. Refractive index varies with frequency, with higher frequencies having slightly higher refractive indexes. This explains the bending of different colored light in prisms, producing a rainbow.

What I'm having trouble with is how this relates to the equation n = c/v. If the refractive index increases with frequency, from the equation you would get a decrease in v, implying that higher frequency light travels at a slower velocity. But I thought all wavelengths of light travel at the same speed? (v = f*lambda)

 

[dayumgina]

So the first thing you have to recall is that frequency never changes in a different medium whereas velocity and and wavelength will. For instance, if there were different waves in one medium, they would all have the same velocity, and if the same wave was in different media, it would have different velocities relative to the medium. Frequency doesn't change, so it's actually the wavelength that changes as you go from one n to another.

Back to the prism, the "fastest" colored light will be red and the slowest violet. This is because the longest wavelength, red, will bend the least and that's why it'll go through the prism first. In general shorter wavelengths (i.e. light towards the blue end of the spectrum) have higher indices of refraction and get bent more than light with longer wavelengths (towards the red end).

Hope that helps, sorry if I confused you further.

This has been bugging me. Refractive index varies with frequency, with higher frequencies having slightly higher refractive indexes. This explains the bending of different colored light in prisms, producing a rainbow.

What I'm having trouble with is how this relates to the equation n = c/v. If the refractive index increases with frequency, from the equation you would get a decrease in v, implying that higher frequency light travels at a slower velocity. But I thought all wavelengths of light travel at the same speed? (v = f*lambda)

 

[oxeye]

This has been bugging me. Refractive index varies with frequency, with higher frequencies having slightly higher refractive indexes. This explains the bending of different colored light in prisms, producing a rainbow.

What I'm having trouble with is how this relates to the equation n = c/v. If the refractive index increases with frequency, from the equation you would get a decrease in v, implying that higher frequency light travels at a slower velocity. But I thought all wavelengths of light travel at the same speed? (v = f*lambda)

If I remember correctly, the n=c/v equation only applies for a given frequency.

All wavelengths of light do not travel at the same speed - it depends on the medium through which they travel. Light travels at c=3*10^8 m/s in a vacuum. It is always slower than that if travelling through something (air, glass, water, etc).

 

[zackscoot]

This has been bugging me. Refractive index varies with frequency, with higher frequencies having slightly higher refractive indexes. This explains the bending of different colored light in prisms, producing a rainbow.

What I'm having trouble with is how this relates to the equation n = c/v. If the refractive index increases with frequency, from the equation you would get a decrease in v, implying that higher frequency light travels at a slower velocity. But I thought all wavelengths of light travel at the same speed? (v = f*lambda)

I think you got the concept WRONG... Index of refraction is not related to the frequence or the wavelength of a particular light!!!! Index of refraction is the property of the medium which light travel in. So higher frequence does not mean that it will have higher index of refraction (since index of refraction is an intrinsic property of the medium and not of the light!!!).

What index of refraction is is just the RATIO of the speed of light in vacuum to the speed of light in a particular medium (glass, air etc)... and again it depends on the property of the medium.

You mentioned something about rainbow and splitting white light into different colors. THAT IS NOT REFRACTION!!!! that is called dispersion. Those two things are completely different. In the case of dispersion, the higher the frequence, the less likely it will bend when it comes out of the prism.


JUST REMEMBER: FREQUENCY OF LIGHT HAS NOTHING TO DO WITH THE VALUE OF INDEX OF REFRACTION!!! HIGH FREQUENCY DOES NOT MEAN HIGH INDEX OF REFRACTION. INDEX OF REFRACTION IS CONSTANT FOR A GIVEN MEDIUM... SO AIR HAS AN INDEX OF 1.02, GLASS I THINK HAS A VALUE OF 1.2.... SO REGARDLESS OF WHAT FREQUENCY OR WAVELENGTH THE LIGHT HAS, THE INDIX WILL NEVER CHANGE

 

[Surf Rx]

All wavelengths/frequencies of light do travel at the same speed...in a vacuum. Usually the speed of a wave is determined by the medium and not the frequency. However, this doesn't hold true for light waves through a material medium. Higher frequency light travels slower through a material medium and will therefore have a greater index of refraction, which will cause it to refract more. That's why blue light bends more than red light when travelling through a prism. This concept is called dispersion. For more info...http://en.wikipedia.org/wiki/Dispersion_(optics)

 

[Tensyle]

I think you got the concept WRONG... Index of refraction is not related to the frequence or the wavelength of a particular light!!!! Index of refraction is the property of the medium which light travel in. So higher frequence does not mean that it will have higher index of refraction (since index of refraction is an intrinsic property of the medium and not of the light!!!).

What index of refraction is is just the RATIO of the speed of light in vacuum to the speed of light in a particular medium (glass, air etc)... and again it depends on the property of the medium.

You mentioned something about rainbow and splitting white light into different colors. THAT IS NOT REFRACTION!!!! that is called dispersion. Those two things are completely different. In the case of dispersion, the higher the frequence, the less likely it will bend when it comes out of the prism.


JUST REMEMBER: FREQUENCY OF LIGHT HAS NOTHING TO DO WITH THE VALUE OF INDEX OF REFRACTION!!! HIGH FREQUENCY DOES NOT MEAN HIGH INDEX OF REFRACTION. INDEX OF REFRACTION IS CONSTANT FOR A GIVEN MEDIUM... SO AIR HAS AN INDEX OF 1.02, GLASS I THINK HAS A VALUE OF 1.2.... SO REGARDLESS OF WHAT FREQUENCY OR WAVELENGTH THE LIGHT HAS, THE INDIX WILL NEVER CHANGE

coherent response, but damn, simmer down.

 

[quiksilver87]

coherent response, but damn, simmer down.

it's science...everyone tends to get a little over excited!

 

[Descarteo]

This concept is so confusing...but ive streamlined my understanding of it to wavelength and speed. we know that v=f*(wavelength), therefore speed increases with wavelength. So, consider violet (shorter wavelength) and red (longer wavelength), passing from air to glass, the one with longer wavelength, and thus, higher speed would be expected to deflect less (or bend less) cos it passes thru faster. Therefore, Red(longer wavelenth) bends less, and violet(shorter wavelength) bends more.