What happens to wavelength and frequency when a wave changes velocity

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When an EM wave goes into say a denser medium and its velocity is decreased how does its wavelength and frequency change? I read that the frequency remains constant but the wavelength changes. Is this true? If so does that mean the wave gets compressed when it enters a denser medium. Does the amplitude decrease too?
 
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The index of refraction specifically states the change in wave-length for a em-wave.

[tex]n=\frac{\lambda}{\lambda_{n}}[/tex]

and the relation for velocity-a medium- and light is

[tex]n=\frac{c}{v}[/tex]

that gives a simple answer to your question. does it help?
 
Or if you wish to think of it "graphically" then imagine a wave heading into an object, say glass at a specific angle. What happens to the first part of the wave that hits the glass?... you can think of it like the first part of the wave gets slowed down, before the other part catches up. Now draw this, and you'll notice that the waves tend to get bunch up. Now make deductions based on the fact that you know the velocity has decreased.
 
Ah yeah that explains it thanks. I do like to understand things visually first then use the mathematical approach to verify my understanding and unravel things I wouldn't have spotted.