Refractive index & Critical angles

Notice the mirror effect at the water-air boundary - this is caused by total internal reflection

Every transparent material has a refractive index. What is a refractive index? [1]
- The ratio of speed of light in a vacuum to sped of light in that medium
  - What is the formula to calculate the refractive index of a material? [1]

Is the refractive index different for different colours of light? [1]
- Yes!
  - Why? [1]
    - Red light slows down the least when it travels from air into glass, so it is refracted the least
      - Which visible colour has the lowest refractive index? [1]
        
        Red (i.e. Refractive index in glass = 1.514)
      - Which visible colour has the highest refractive index? [1]
        
        Violet (i.e. Refractive index in glass = 1.528)
What does Snell's Law tell us? [1]
- According to snell's law, the angle of incidence, angle of refraction and refractive index are all linked
  - How exactly are they linked? [1]
    - refractive index (n) = sine of the angle of incidence (i) / sine of the angle of refraction (r)
      - What is the short-hand form of the formula? [1]
        
        n = sin i / sin r
        
        A beam of light travels from air into water. the angle of incidence is 23º. What is the angle of refraction? (the refractive index for water is 1.33) [3]
        
        formula: n = sin i / sin r
        
        rearrange: sin r = sin i / n
        
        substitue: sin r = sin 23 / 1.33
        
        solve: sin r = 0.29
        
        rearrange: r = sin-¹ (0.29)
        
        solve: r = 17º

How does the speed change when light leaves a material with a higher refractive index (i.e. glass, 1.5) and enters a material with a lower refractive index (e.g. air, 1)? [1]
- It speeds up
  - So which way does the light bend; toward or away from the normal? [1]
    - away from the normal
      - What happens to the angle of refraction if you increase the angle of incidence? [1]
        
        It gets larger and the ray moves further away from the normal
        
        What is the angle of incidence called when the angle of refraction reaches 90º and is refracted right along the boundary? [1]
        
        The critical angle (C)
        
        What happens if you make the angle of incidence greater than the critical angle? [1]
        
        You get total internal reflection (no light leaves the medium)
        
        Does total internal reflection have to do with reflection or refraction? [1]
        
        Refraction. It only appears similar to reflection but is in fact caused by refraction
        
        Is a ray travelling from a less optically-dense media (i.e. air) into a more optically-dense media (i.e. glass) able to be totally internally reflected? [1]
        
        No - this would cause the ray to slow down and move towards the normal.
        
        What happens if you make the angle of incidence less than the critical angle? [1]
        
        Most of the light passes out (refracted)
        
        What happens if you make the angle of incidence equal to the critical angle? [1]
        
        The emerging ray comes out along the surface. There's quite a bit of internal reflection (but not total)
        
        Is the critical angle the same for all materials? [1]
        
        No - different materials have different critical angles (e.g. Glass has a critical angle of 42º)
        
        What is the equation to calculate the critical angle of a material? [1]
        
        sine of the critical angle (C) = the refractive index of the material the light's travelling towards (n_r) / the refractive index of the material the light starts from (n_i)
        
        What is the short-hand form of this formula? [1]
        
        sin C = n_r / n_i
        
        What happens to the Critical angle if the refractive index of the material is higher? [1]
        
        The higher the refractive index, the higher the critical angle (e.g. water, C = 49º)
        
        E.g. Jacob does an experiment to find out the refractive index of his strawberry flavour jelly. He finds that the critical angle for a light beam travelling from his jelly into air is 42º. Calculate the refractive index of Jacob's Jelly.
        
        constants:
        
        sin C = sin 42 = 0.72
        
        n_air = 1
        
        formula: sin C = n_air / n_jelly
        
        rearrange: n_jelly = n_air / sin C
        
        substitute: n_jelly = 1 / 0.72
        
        solve: n_jelly = 1.39
        
        E.g.2. Calculate the critical angle for a light beam travelling from glass with a refractive index of 1.52 into air.
        
        constants:
        
        n_air = 1
        
        n_glass = 1.52
        
        formula: sin C = n_air / n_glass
        
        substitute: sin C = 1 / 1.52
        
        solve: sin C = 0.66
        
        rearrange: C = sin-¹ (0.66)
        
        solve: C = 41º

How do optical fibres work? [1]
- Total Internal Reflection - a wave enters one end of the fibre and it is reflected repeatedly until it emerges at the other end
  - Light always travels in straight lines, but optical fibres can be bent! How does it 'bend' light? [1]
    - Optical fibres can be bent, but not sharply, or the angle of incidence might fall below the 'critical angle' (and the light would not totally internally reflect)
  - What kinds of light waves do optical fibres use? [2]
    - Visible or Infrared light
  - What is the thin inner core usually made from? [2]
    - Glass or plastic

Classwork
- 1) Write down the formula for refractive index in words
- 2) Which of these colours is refracted the least: Violet, Green, blue, red, orange?
- 3) For which colour light does glass have the highest refractive index - violet, green or red?
- 4) Write down Snell's law
- 5) A beam of light enters a material with i = 30º. It refracts so that r = 20º. What is the refractive index of the material?
- 6) Explain what is meant by 'total internal reflection'
- 7) The critical angle for glass is approximately 42º. Charlie says the angle of incidence shown in this diagram is 49º. Is he correct? (Explain how you know)
- 8) Explain why sending data by optical fibre might be better than broadcasting it as a radio signal
- 9) Find the critical angle of a liquid-air boundary if the refractive index of the liquid is 1.35

Homework
- 1) Doctors can use an endoscope to look inside a patient's body. An endoscope has two bundles of optical fibres - one carries light down into your stomach, say, and the other returns the reflected light back to a monitor. Optical fibres work because of total internal reflections.
  - Explain why doctors must be careful not to bend an endoscope sharply
- 2) Below is a diagram of a ray of light entering a material with refractive inex n.
  - Copy and Label the following parts of the diagram: (Incident ray, Normal line, Refracted ray, Angle of incidence, Angle or refraction)
  - Snell's law relates the refractive index, n, to the two angles i and r. Write down Snell's law.
- 3) A light ray was shone from air into some water. The ray had an angle of incidence of 30º and an angle of refraction of 22º.
  - Use this data to calculate the refractive index of water (show your working)
- 4) The diagram shows white light undergoing dispersion when it refracts from air into glass
  - The refractive index in glass for red light is 1.514. Calculate the angle of refraction for red light
  - The refractive inex in glass for blue light is 1.528. What does this tell you abou the speed of blue light in glass compared to red light?
- 5) Light passes through th acrylic bottom of a boat into the water below. For blue light, the refractive index of acrylic is 1.498 (4 s.f.) and the refractive index of water is 1.337 (4 s.f.)
  - What happens to the speed of the light as it passes into the water?
  - Complete this sentence by choosing the correct option in brackets: "The angle of refraction is ................. ( greater than / less than ) the angle of incidence"
  - If the angle of incidence were equal to the critical angle, what would the angle of refraction be?
  - What happens to light which enters the water at an angle greater than the critical angle?
  - Calculate the critical angle for the acrylic to water boundary for blue light, to the nearest degree (hint: you'll need the equation with 'sinC' in it)

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Refractive index & Critical angles

Notice the mirror effect at the water-air boundary - this is caused by total internal reflection

Every transparent material has a refractive index. What is a refractive index? [1]

Is the refractive index different for different colours of light? [1]

What does Snell's Law tell us? [1]

How does the speed change when light leaves a material with a higher refractive index (i.e. glass, 1.5) and enters a material with a lower refractive index (e.g. air, 1)? [1]

How do optical fibres work? [1]

Classwork

Homework