Two Chapter 8

• If the velocity decreases, then the wavelength decreases and the frequency remains the same (frequency is determined by the source).
• The speed of a wave changes when it moves from one medium to another, therefore, wavelength changes but frequency does not because the wave still has the same source.
• Therefore:

• When a wave meets the boundary between media, its direction may change.

As the wave moves into the slower As the wave moves into the faster

medium in a time equal to the period medium in a time equal to the period

the wave moves less distance the wave moves a greater distance

therefore, the wave bends. therefore, the wave bends.

• Refraction – the change in direction of a wave as it changes speed in moving from one medium to the next.
• When moving from a fast to slow medium.
  1. refraction is towards the normal
  2. wavelength decreases
  3. velocity decreases
  4. frequency remains the same
• When the wave moves from slow to fast
  1. refraction is away from the normal
  2. wavelength increases
  3. velocity increases
  4. frequency remains the same

• This is the Law of Refraction (sometimes called Snell's Law).
• Relative Index of refraction – the ratio of the speed of a wave in one medium to the speed of the wave in another medium.
• n₁₂ – relative index of refraction for a wave moving from medium 1 to medium 2
• n₃₂ – relative index of refraction for a wave moving from medium 3 to medium 2
• Absolute Index of Refraction – the ratio of the speed of an electromagnetic wave in a vacuum to its speed in a medium
• n₂ – the absolute index of refraction of medium 2.
• n₁ – the absolute index of refraction of medium 1.
• Since frequency remains constant, one would expect that the amount of refraction is the same regardless of the frequency. There are however, exceptions.
• Dispersive Medium – a medium in which the speed of the wave depends upon the frequency.
  • causes waves of different frequency to refract through different angles given all have the same angle of incidence.
• We previously stated that wave speed is determined by the characteristics of the medium.
  • This is a good approximation and is true under ideal circumstances.
  • Changes in speed due to frequency are small and often go unnoticed.
• When refraction occurs, some of the incident wave is always reflected (most evident when the wave moves from slow to fast medium).
• In a slow to fast movement, the angle of incidence is always less than the angle of refraction.
  • As the angle of incidence gets larger, the angle of refraction will reach 90^o before the angle of incidence gets to 90^o.
  • Further increases of the angle of incidence cause no refraction and only reflection.
• Critical Angle – the angle of incidence that produces an angle of refraction of 90^o.
  • If the angle of incidence is greater than the critical angle, then 100% reflection occurs.
  • If the angle of incidence is less than the critical angle, then some reflection and some refraction occurs (partial reflection and refraction).
• To calculate the critical angle;
  • substitute 90^o for the angle of refraction into the law of refraction and calculate the angle of incidence.
  • This calculated angle of incidence is the critical angle.
• Total Internal Reflection – reflection off of a boundary between media when the angle of incidence is greater than the critical angle.
  • Can only occur when the wave moves from a slow to a fast medium.

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November 7, 2013