1. CfE Higher Physics Particles and Waves
“Anyone who is not shocked by the quantum theory has not understood it.“ N.Bohr

2. Key Areas Key Area – Refraction of Light Absolute refractive index.
Critical Angle and Total Internal Reflection.
Lenses and optical Instruments.

3. Learning Intentions State what is meant by refraction.
Explain why refraction occurs.
Indicate on a diagram the angles of incidence and refraction.
Explain what happens to the speed, wavelength and frequency of light during refraction.

4. Refraction Definition:
Refraction is the change in direction of a wave as a result of its change in speed as it moves from one medium to another.
Each medium must have a different optical density for refraction to occur.

5. Refraction
A medium is the substance that the light is travelling through.
Angle of Incidence
Glass Block
Air
Incident Ray

6. Refraction
Glass Block
Refracted Ray
The change in direction of the light at each boundary is called refraction.
Angle of Incidence
Angle of Refraction
Air
Incident Ray

7. Normal Incidence What is the angle of incidence here? Incident Ray
Glass Block
Air

8. Normal Incidence Why is there no change of direction now? Incident Ray
Glass Block
Air

9. Refraction
Refraction is caused by the change in the speed of light, but it only happens when the angle of incidence is greater than zero.
Analogy 1
Analogy 2

10. Refraction and Optical Density
When entering an optically more dense medium at an angle to the normal, a wave will bend towards the normal.
When travelling into an optically less dense medium at an angle to the normal, a wave will bend away from the normal.
Glass Block
Air

11. Refraction: Speed, Wavelength and Frequency
When light waves travel between two media with different optical densities, their speed and wavelength both change.
The frequency, however, remains the same. The frequency of light depends only on the light source.
Consider the relationship;
When the speed decreases and the wavelength decreases, the frequency can remain constant.
Lower speed, shorter wavelength, same frequency!

13. Refractive Index (n)
The amount of refraction that occurs depends on the refractive index of the 2 media that the light is passing through.
If the refractive index of both materials is the same then no refraction will occur.
Different materials have different refractive indices:
There is a positive correlation between density and refractive index.

14. Learning Intentions Define refractive index.
Carry out calculations to find the refractive index of a material.
Define and explain absolute refractive index.
State the absolute refractive index of a vacuum and compare it to that of air.
Understand the relationship between refractive index, wavelength and wave speed.
Explain what is meant by the principle of reversibility of light.
State Snell’s Law.

15. Refractive Index (n)
From the geometry of refraction, we can deduce that the refractive index of a material is the ratio of the sine of the angle in the less dense medium to the sine of the angle in the more dense medium:
Glass Block
Air

16. Example
A ray of light passes through a glass block. The angle of incidence in the air is 35° and the angle of refraction in the glass is 25°. Calculate the refractive index of the glass.
Glass Block
Air

17. Example
Light enters water and illuminates a fish. Light from the fish emerges from the water and enters an observer’s eye. As it passes into the air, it refracts. Calculate the refractive index of the water.

18. Absolute Refractive Index
In class experiments to determine the refractive index of a material, we assume that the refractive index of the air is the same as that of a vacuum. This assumption is justifiable given the accuracy of the measurements.
When a high degree of precision is needed, absolute refractive index should be considered.
Definition:
The absolute refractive index of a material is the ratio of the speed of light in that material to the speed of light in a vacuum.
The absolute refractive index for a material is always greater than 1.

19. Absolute Refractive Index
Light travels slightly slower in air than in a vacuum meaning that the Sun’s light will refract slightly when it enters the Earth’s atmosphere.
The refractive index of a material determined in air will be slightly different from the absolute refractive index.
The absolute refractive index of a vacuum is 1 and for air it is , so for practical purposes they are often taken to be the same.

20. Absolute Refractive Index
The refractive index varies very slightly with the frequency of the waves.
Typical types of glass will have a refractive index about 1% higher for blue light than red.

21. Refraction at a boundary between 2 media.
Refraction can occur when light travels from one medium to another where neither medium is air or a vacuum.
In this example, the medium with the lower refractive index has an absolute refractive index, n1.
The relationship can then be written:
This gives the refractive index of the more optically dense medium relative to the less optically dense medium determined when light travels from n1 to n2.
N.B. In calculations, θ1 is always the angle in the less dense medium.

22. Refraction at a boundary between 2 media.
Using geometry, it can be proven that:
Given that;
and the frequency is constant, it follows that;

23. Principle of Reversibility of Light
When a ray of light is reflected or refracted, it will follow exactly the same path if its direction is reversed.

24. Principle of Reversibility of Light
For refraction and the calculation of the refractive index, it can be shown... θ1 θ2

25. Snell’s Law Snell’s Law:
This law of refraction was named after Dutch astronomer Willebrord Snellius ( ), but it had been discovered much earlier in 984 in Baghdad by Ibn Sahl.
Snell’s Law:
The ratio of the sines of the angles of incidence and refraction of a wave are constant when it passes between two given media.
i.e.

26. What do you think?
At the water-air interface, the light from below the surface reflects back.
The light from above the surface cannot penetrate through the surface of the water.
The water is less transparent than the air.
The sunlight refracts as it enters the water, making it impossible to see through the surface.

27. Learning Intentions
Sketch ray diagrams for a semi-circular glass block which show refraction, total internal reflection and the scenario of the critical angle.
Define the term ‘critical angle’.
Calculate critical angle from the refractive index.
Optical fibres as an application of TIR and use of materials of different refractive indices.

28. Semi-Circular Block Small Angle of Incidence
Aim the incident ray at the centre of the flat surface.
Glass Block
Small Angle of Incidence
Air
Incident Ray

29. Refraction – Semi-Circular Block
Angle of Refraction
Refracted Ray
Glass Block
Why is there no change of direction here?
Small Angle of Incidence
Air
Incident Ray

30. Refraction – Semi-Circular Block
Refracted Ray
Glass Block
Air
Upon careful inspection you will notice some reflection.
Weak Reflected Ray
Incident Ray

31. Semi-Circular Block Large Angle of Incidence
Why do you think this is called Total Internal Reflection?
Air
Large Angle of Incidence
Angle of Reflection
Incident Ray
Glass Block
ReflectedRay
How do we know this is reflection?

32. Semi-Circular Block Critical Angle
When the angle of incidence is equal to the critical angle, the angle of refraction is 90° and the refracted ray travels along the boundary.
Refracted Ray
Incident Ray
Angle of Incidence =
Critical Angle
Reflected Ray
Glass Block
Air

33. Refraction, Total Internal Reflection and the Critical Angle
When the angle of incidence is small, the light refracts across the boundary into the air. Some light is reflected.
When the angle of incidence is large, total internal reflection occurs: All the light remains in the glass.
At an angle of incidence called the critical angle, which is specific to that material, the angle of refraction is exactly 90° and the refracted ray travels along the boundary.

34. Summary: Critical Angle and Total Internal Reflection
Use to recap previous experiment

35. Snell’s Law and the Critical Angle
Using Snell’s Law and the Principle of Reversibility of Light:
For the Critical Angle:

36. Optical Instruments using Total Internal Reflection - Periscope

37. Optical Instruments using Total Internal Reflection - Binoculars

38. Optical Instruments using Total Internal Reflection – SLR Camera

39. Reflective Road Signs
Reflective road signs use ‘retroreflection’ – they send light back where it came from.
Total internal reflection happens in glass beads which are in the paint or plastic of the on the sign.
This is also how cat’s eyes work.

40. Optical Fibres
Optical fibres are long thin strands of glass which carry light signals using total internal reflection.
They can be used to carry coded data for internet and phones.

41. Optical Fibres
They can also be used to transmit light in endoscopes which allow visual examination of a patient.

42. Optical Fibres
They are constructed of 2 types of glass (core and cladding), each with different refractive indicies.
Total internal reflection occurs at the boundary between the 2 types of glass.

43. Optical Fibres
The core has a higher refractive index than the cladding.
This means that light shining along the core and striking the boundary at a large angle of incidence will totally internally reflect.

44. Example
The absolute refractive index of a semi-circular block of glass is 1.47.
Calculate the critical angle for this glass block.
Glass Block
Air
Critical Angle

45. The minimum angle is the critical angle.
Example
The core (n=1.50) has a higher refractive index than the cladding (n=1.45).
Calculate the minimum angle of incidence at the core-cladding boundary that will allow a signal to be transmitted through the fibre.
Cladding n1 = 1.45
Core n2 = 1.50
The minimum angle is the critical angle.

46. Dispersion in Optical Fibres
Dispersion creates problems for signal transmission. This causes signal attenuation with distance in the fibre.
Chromatic Dispersion: The refractive index depends on the frequency. If the signal is composed of a range of frequencies then this will cause the colours to separate slightly.
Modal Dispersion: Light can take longer or shorter paths through the fibre. This casues the signal to be spread out in time.

47. Diamonds
Diamond have a very high absolute refractive index of around 2.42.
Calculate the Critical Angle for Diamond:

48. Why do Diamonds sparkle?
A high refractive index means a small critical angle.
This means that light is more likely to be totally internally reflected within the diamond.
This light is then refracted back out through the top surface of the gem making the diamond sparkle.

49. Why do Diamonds Sparkle?
This effect can be enhanced by the cut of the diamond.
The cut affects the angle of incidence of the light in the diamond.

50. Why can we see colours in a diamond?
Each colour in white light refracts by a different amount. The refractive index varies with the frequency of the light.
After refraction and multiple internal reflections, some colours will have travelled further than others.
The further the light travels, the more the colours separate or disperse.