Is speed of em waves directly proportional to magntiude of wavelength

[sgstudent]

I read that speed is directly proportional to wavelength in a medium. so does it mean that gamma is the slowest in air compared to the rest of the waves?

 

[Simon Bridge]

Not really. The speed of em waves is a constant.

But you are thinking in terms of propagation through a medium, using the wave model for light and you'd be correct - gamma waves are slower than, say, any visible light waves. Also means they bend the most at interfaces.

 

[sgstudent]

Oh okay thanks for the help! But isn't propagation the same as just existing?

 

[Jasso]

I think what Simon Bridge is saying is that the speed of propagation through a medium is dependent on frequency, with emphasis on "through a medium".

The ratio of the speed of light in a vacuum to the speed of propagation through a medium is the index of refraction for that medium. The fact that it is different for different frequencies is known as dispersion, and gives rise to effects like the splitting of light through a prism.

 

[Simon Bridge]

@Jasso: that's exactly what I'm saying - thanks.

Of course it is possible to exist and not propagate... that's what birth-control is for.

 

[mfb]

I think what Simon Bridge is saying is that the speed of propagation through a medium is dependent on frequency, with emphasis on "through a medium".

That is right, but the dependence is complicated and no where near "linear". In good approximation, all wavelengths have the speed of c in air, which is the same as they have in a vaccum.

Now, the influence of air on gamma rays is quite small (refractive index a bit smaller, but close to 1), whereas smaller frequencies get a bigger impact (and a refractive index larger than 1).
The group velocity is a bit different, but this should be a bit larger for gamma rays as well.

In solid objects, the difference in the refractive index is easier to see: Gamma rays pass through prisms without a significant modification, while visible light changes its direction.