1. Reflection and Refraction
Chapter 30
Reflection and Refraction

2. Geometric Optics and Ray Approximation
Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media
The ray approximation is used to represent beams of light – a ray of light is an imaginary line drawn along the direction of travel of the light beams
A wave front is a surface passing through points of a wave that have the same phase
The rays, corresponding to the direction of the wave motion, are perpendicular to the wave front

3. Geometric Optics and Ray Approximation
Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media
The ray approximation is used to represent beams of light – a ray of light is an imaginary line drawn along the direction of travel of the light beams
A wave front is a surface passing through points of a wave that have the same phase
The rays, corresponding to the direction of the wave motion, are perpendicular to the wave front

4. Specular Reflection
Specular reflection is reflection from a smooth surface
The reflected rays are parallel to each other
All reflection in this chapter is assumed to be specular

5. Diffuse Reflection
Diffuse reflection is reflection from a rough surface
The reflected rays travel in a variety of directions
Diffuse reflection makes the dry road easy to see at night

6. Law of Reflection
The normal is a line perpendicular to the surface at the point where the incident ray strikes the surface
The incident ray makes an angle of θ1 with the normal and the reflected ray makes an angle of θ1’ with the normal
The angle of reflection is equal to the angle of incidence:
θ1= θ1’

7. Refraction of Light
When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium
The ray that enters the second medium is refracted – bent at the boundary

8. Refraction of Light
The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane
The angle of refraction, θ2, depends on the properties of the medium and the angle of incidence
The path of the light through the refracting surface is reversible

9. Refraction of Light Ray  is the incident ray
Ray  is the reflected ray
Ray  is refracted into the crystal
Ray  is internally reflected in the crystal
Ray  is refracted as it enters the air from the crystal

10. Refraction of Light
Light may refract into a material where its speed is lower
The angle of refraction is less than the angle of incidence so the ray bends toward the normal

11. Refraction of Light
Light may refract into a material where its speed is higher
The angle of refraction is greater than the angle of incidence so the ray bends away from the normal

12. The Index of Refraction
When light passes from one medium to another, it is refracted because the speed of light is different in the two media
The index of refraction, n, of a medium can be defined
n is a unitless ratio
For a vacuum, n = 1 whereas for other media, n > 1

13. The Index of Refraction
The wavefronts do not pile up, nor are created or destroyed at the boundary
Therefore, as light travels from one medium to another, its frequency does not change
Both the wave speed and the wavelength do change

14. The Index of Refraction
v1 = ƒ λ v2 = ƒ λ2
The ratio of the indices of refraction of the two media can be expressed as various ratios

15. Snell’s Law of Refraction
Willebrord Snel
van Royen
1580 – 1626
Snell’s Law of Refraction
n1 sin θ1 = n2 sin θ2

16. Chapter 30 Problem 35
You’re standing 2.3 m horizontally from the edge of a 4.5-m-deep lake, with your eyes 1.7 m above the water’s surface. A diver holding a flashlight at the lake bottom shines the light so you can see it. If the light in the water makes a 42° angle with the vertical, at what horizontal distance is the diver from the edge of the lake?

17. Atmospheric Refraction
There are many interesting results of refraction in the atmosphere
At sunsets, light rays from the sun are bent as they pass into the atmosphere
It is a gradual bend because the light passes through layers of the atmosphere, and each layer has a slightly different index of refraction
The Sun is seen to be above the horizon even after it has fallen below

18. Atmospheric Refraction
A mirage can be observed when the air above the ground is warmer than the air at higher elevations
The rays in path B are directed toward the ground and then bent by refraction
The observer sees both an upright and an inverted image

19. Atmospheric Refraction

20. Polarization by Reflection
When an unpolarized light beam is reflected from a surface, the reflected light can be completely polarized, partially polarized, or unpolarized
It depends on the angle of incidence
If the angle is 0° or 90°, the reflected beam is unpolarized
For angles between this, there is some degree of polarization
For one particular angle, the beam is completely polarized

21. Polarization by Reflection
The angle of incidence for which the reflected beam is completely polarized is called the polarizing (or Brewster’s) angle, θp
Brewster’s Law relates the polarizing angle to the index of refraction for the material
Sir David Brewster
1781 – 1868

22. Total Internal Reflection
Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction
Ray 5 shows internal reflection

23. Critical Angle
A particular angle of incidence (critical angle) will result in an angle of refraction of 90°
For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary
This ray obeys the Law of Reflection at the boundary

24. Chapter 30 Problem 48
Find a simple expression for the speed of light in a material in terms of c and the critical angle at an interface between the material and vacuum.

25. Fiber Optics Utilizes internal reflection
Plastic or glass rods are used to “pipe” light from one place to another
Applications include diagnosis and correction of medical problems, telecommunications, etc.

26. Dispersion
The index of refraction in anything except a vacuum depends on the wavelength of the light
This dependence of n on λ is called dispersion
Snell’s Law indicates that the angle of refraction made when light enters a material depends on the wavelength of the light
The index of refraction for a material usually decreases with increasing wavelength

27. Refraction in a Prism
The amount the ray is bent away from its original direction is called the angle of deviation, δ
Since all the colors have different angles of deviation, they will spread out into a spectrum: violet deviates the most and red deviates the least

28. Spectroscopy
A prism spectrometer uses a prism to cause the wavelengths to separate (to study wavelengths emitted by a light source)
All hot, low pressure gases emit their own characteristic spectra with the particular wavelengths emitted by a gas serving as “fingerprints” of that gas
Spectral analysis: identification of molecules, minerals, elements in distant stars, etc.

29. The Rainbow
A ray of light strikes a drop of water in the atmosphere and undergoes both reflection and refraction
First refraction at the front of the drop: violet light will deviate the most and red – the least
At the back surface the light is reflected and refracted again as it returns to the front surface and moves into the air
The rays leave the drop at various angles

30. The Rainbow
If a raindrop high in the sky is observed, the red ray is seen
A drop lower in the sky would direct violet light to the observer
The other colors of the spectra lie in between the red and the violet

31. Answers to Even Numbered Problems
Chapter 30:
Problem 12 4

32. Answers to Even Numbered Problems
Chapter 30:
Problem 36
1.3 m

33. Answers to Even Numbered Problems
Chapter 30:
Problem 38
42°