# Change in length of an electromagnetic wave

## Homework Statement

An electromagnetic wave, which has the frequency of f = 5MHz, goes from an unpermeable location, which has a permittivity of e = 2, to vacuum. Calculate the change in length of the wave.
NOTE: I haven't found greek letters in the post menu, so if they're somewhere in there tell me! I could fix the post then.

## The Attempt at a Solution

Okay my first approach would be to calculate the length of the wave in vacuum, so: (mainly because it's easier)

L1 = c * T;

T = 1 / f

L1 = c / f

L1 = 3 * 108 / 5 * 106 = 60 m

Then i would calculate the length of the wave in the previous location (the unpermeable one):

L2 = v / f

For electromagnetic waves (if i recall correctly) we can use this formula to calculate their speed:

v = 1 / sqrt e * µ (where e is the permittivity and µ is permeability of the area)

Here's where my guess comes in. I guess that unpermeable areas do not have any permeability? So it would mean:

v = 1 / sqrt e

But then the length of the wave would be insanely small. I know that waves should be short, but the difference should clearly be bigger.

Am i wrong or right?