30. Reflection & Refraction

2 Topics The Speed of Light Reflection, Refraction Polarization Revisited Spectroscopy

3 Speed of Light The first hint that light traveled at a finite speed came from measurements of the period of Jupiter’s moon Io

4 Speed of Light Ole Rømer’s Method (1675) (Römer, Roemer) When the Earth was at point C the eclipses of Io were observed to be later than predicted by about 16.6 minutes

5 Speed of Light Rømer’s Method (1675) Rømer reasoned that this must be due to the time it takes light to traverse the diameter of the Earth’s orbit

6 Speed of Light Today, the speed of light is defined to be exactly c = m/s The meter is now defined to be the distance traveled by light in vacuum in 1/ s

7 Speed of Light Distances in astronomy are so great that it is customary to use the distance traveled by light in a given time as a unit of distance Examples – distance from Earth to: 1. Moon1.25 light-seconds 2. Sun8.33 light-minutes 3. Pluto5.5 light-hours 4. Alpha Centauri4.5 light-years (ly) 5. Andromeda2.1 million ly

8 Fermat’s Principle Light travels from one point to another along the path of least time Note: The path of least time is not necessarily the shortest path

Reflection & Refraction

10 Reflection & Refraction The speed of light v in a transparent medium is less than its speed c in vacuum. Such media are characterized by an index of refraction, n For water n = 1.33 For glassn = 1.5 to 1.66

11 Frequency Between Media As light travels from one medium to another, its frequency does not change But the wave speed and the wavelength do change The wave fronts do not pile up at the boundary, so the ƒrequency must stay the same

12 Reflection & Refraction Law of Reflection: angle of reflection = angle of incidence

13 Reflection & Refraction Snell’s Law of Refraction (Willebrord Snel van Royen, 1621) Angle of refraction

14 Example: Refraction from Air to Water Air:n 1 = 1 Water:n 2 = 1.33  1 = 45 o

15 Reflection & Refraction As the angle of incidence is increased a critical angle of incidence  c is reached at which the angle of refraction is 90 o.

16 Total internal Reflection If the angle of incidence is is greater than the critical angle  c there is no refracted ray. All the light is reflected. This is called total internal reflection. This requires n 1 > n 2

Examples of Reflection and Refraction

18 Light can be transmitted along transparent glass fibers using total internal reflection. Such fibers are used in imaging and form the backbone of the internet and other telecommunications Fiber Optics

19 Mirages These are caused by a continuous change in the index of refraction of a medium, which leads to the gradual bending of light

20 Dispersion The index of refraction depends slightly on the wavelength. This causes light comprising an admixture of wavelengths, e.g., white light, to be dispersed into the different wavelength components

21 Index of Refraction versus Wavelength The index of refraction for a material usually decreases with increasing wavelength Violet light refracts more than red light when passing from air into a denser material

That’s Why the Sky is Blue! 22 The parish of Soufrière, Dominica

23 Rainbows Reflection inside rain drop at the back surface Followed by refraction on leaving rain drop Net angle of deviation depends on color: violet deviates by 40° red deviates by 42°

24 Rainbows

25 Rainbows Red appears on the outermost ring of rainbow, while violet appears on the innermost ring.

Polarization Revisited

27 Polarization Polarization by Absorption A polarizer is a device that allows only waves of a given polarization through. y x z

28 Polarization Polarization by Reflection Electromagnetic radiation cannot be emitted in direction of the oscillating electric field, so there is no reflected ray when tan  p = n 2 /n 1 y x z

29 Spectroscopy Hydrogen Helium Barium Mercury Continuous spectrum

30 Summary Speed of light in vacuum m/s (by definition) Reflection and refraction Occur at media boundaries Snell’s law n 1 sin  1 = n 2 sin  2 Total internal reflection n 1 sin  c = n 2 Dispersion n varies with wavelength Polarization by absorption and reflection