Describe how the properties of the original wave may change as it is transmitted through a new medium?

Note: the question is incomplete and does not mention what type of wave we are talking about; I will assume that we are talking about a light wave.

When a light wave is transmitted through a new medium, it undergoes a phenomenon called refraction: the direction of the wave as it enters the new medium changes, according to Snell's law

where:

are the index of refraction of the two mediums

are the angle of incidence and angle of refraction, which are the angle between the incoming ray and the normal to the boudary, and the angle between the refracted ray and the normal to the boundary

The index of refraction of a medium is defined as:

(1)

where

c is the speed of light in a vacuum

v is the speed of light in the medium

From eq.(1), it follows that the speed of a light wave changes as it is transmitted through a new medium (in particular, it increases if the wave moves to a new medium with lower refractive index, and it decreases if the wave moves to a new medium with higher refractive index).

On the other hand, the frequency of a wave does not depend on the medium: so, as the wave is transmitted through a new medium, its frequency does not change.

Finally, we can see what happens to the wavelength by looking at the equation:

where is the wavelength, v the speed and f the frequency. As the frequency does not change, we can see that the wavelength changes proportionally to the speed: so, it increases if the speed increases, and it decreases if the speed decreases.

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