Refractive Index

[thais]

I am having a hard time with a concept in Light/Optics.
Could someone please shed some light for me on the effect that frequency has on refractive index? I ran into this statement..
"The refractive index of a transparent medium increases with increasing frequency of the transmitted light."
but I can't get why is that so.
Thank you!

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[Pisiform]

I am having a hard time with a concept in Light/Optics.
Could someone please shed some light for me on the effect that frequency has on refractive index? I ran into this statement..
"The refractive index of a transparent medium increases with increasing frequency of the transmitted light."
but I can't get why is that so.
Thank you!

The idea is simple. As you already know, when light moves from one medium to another, only its speed and wavelength are affected while its frequency remains constant.

Lets consider Red light versus Violet light. Red light has Greatest Wavelength while Violet Light has Smallest wavelength. When both Red and Violet light passes through a medium (say prism), Red light has the greatest speed while Violet light has the slowest speed because v = f Lambda (f is constant and red has higher lambda so high velocity, violet has lowest lambda so lowest velocity).

Formula for RI is n = c / v. Red light has greatest speed which means it has smallest RI so bend less. Violet light has slowest speed and hence greatest RI so bends more. Since violet has the greatest frequency as compares to Red, it safe to assume that High Frequency light has the greatest RI.

 

[thais]

Thank you!
one more question though...
How come the light with larger RI bends more? looking at Snell's law equation I would assume that the light with greater RI would have smaller angle of refraction. Then, does it bend more because this angles are in reference to the normal line?
Thanks!

 

[Pisiform]

because greater RI of that medium means greater angle of refraction but smaller angle of incident. Greater angle of refraction means greater bending.

 

[Erythropoietin]

Thank you!
one more question though...
How come the light with larger RI bends more? looking at Snell's law equation I would assume that the light with greater RI would have smaller angle of refraction. Then, does it bend more because this angles are in reference to the normal line?
Thanks!

Yes, by looking at Snell's law, if you have large n, the angle has to be less. And remember that that angle is the angle from the normal line. So a less angle would mean it bends the most.
So if you have an incident ray coming at an angle of 45 degrees, and if your n is a very large value, the angle will be less and it will bend towards the normal line a lot.
But lets say you have an incoming ray at 45 degrees again, and the n value is not that big..so this means that theta is not as small as it was previously, so it will bend farther away from the normal line

 

[thais]

Thank you!