Chapter 30

1. 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 fromthe 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 λ1 v2 = ƒ λ2 • The ratio of the indices of refraction of the two media can be expressed as various ratios

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

16. Chapter 30Problem 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. Sir David Brewster 1781 – 1868 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

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 30Problem 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 onλ 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°