Chapter 35: Nature of Light and Laws of Geometric Optics

1. Chapter 35: Nature of Light and Laws of Geometric Optics

2. 35.1 The Nature of Light • Before the beginning of the nineteenth century, light was considered to be a stream of particles • The particles were either emitted by the object being viewed or emanated from the eyes of the viewer • Newton was the chief architect of the particle theory of light • He believed the particles left the object and stimulated the sense of sight upon entering the eyes

3. Nature of Light – Alternative View • Christian Huygens argued that light might be some sort of a wave motion • Thomas Young (1801) provided the first clear demonstration of the wave nature of light • He showed that light rays interfere with each other • Such behavior could not be explained by particles

4. More Confirmation of Wave Nature • During the nineteenth century, other developments led to the general acceptance of the wave theory of light • Maxwell asserted that light was a form of high-frequency electromagnetic wave • Hertz confirmed Maxwell’s predictions

5. Particle Nature • Some experiments could not be explained by the wave nature of light • The photoelectric effect was a major phenomenon not explained by waves • When light strikes a metal surface, electrons are sometimes ejected from the surface • The kinetic energy of the ejected electron is independent of the intensity of the light

6. Particle Nature, cont. • Einstein (in 1905) proposed an explanation of the photoelectric effect that used the idea of quantization • The quantization model assumes that the energy of a light wave is present in particles called photons (35.1) • fis the frequency of the electromagnetic wave. • is Planck’s Constant: 6.63 x 10-34 J.s

7. Dual Nature of Light • In view of these developments, light must be regarded as having a dual nature • Light exhibits the characteristics of a wave in some situations and the characteristics of a particle in other situations • Nature prevents testing both qualities at the same time

8. 35.3 The Ray Approximation in Geometric Optics • Geometric optics involves the study of the propagation of light • It uses the assumption that light travels in a straight-line path in a uniform medium and changes its direction when it meets the surface of a different medium or if the optical properties of the medium are non-uniform • The ray approximation is used to represent beams of light

9. Ray Approximation • The rays are straight linesperpendicular to the wave fronts • With the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays

10. Ray Approximation, cont. • If a wave meets a barrier, we will assume that <<d • d is the diameter of the opening • This approximation is good for the study of mirrors, lenses, prisms, etc. • Let’s see when:  ≈ d and  >> d

11. Active Figure 35.4 (SLIDESHOW MODE ONLY)

12. 35.4 Reflection of Light • A ray of light, the incident ray, travels in a medium • When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium • This means it is directed backward into the first medium

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

14. Diffuse Reflection • Diffuse reflection is reflection from a rough surface • The reflected rays travel in a variety of directions • A surface behaves as a smooth surface as long as the surface variations are much smaller than the wavelength of the light

15. Law of Reflection • The normal is a line perpendicular to the surface • It is at the point where the incident ray strikes the surface • The incident ray makes an angle of 1 with the normal • The reflected ray makes an angle of 1’with the normal

16. Active Figure 35.6 (SLIDESHOW MODE ONLY)

17. Law of Reflection, cont. • The angle of reflection is equal to the angle of incidence (35.2) • This relationship is called the Law of Reflection • The incident ray, the reflected ray and the normal are all in the same plane

18. Example 35.1 Double Reflection • Two mirrors make an angle of 120o with each other. An incident ray strikes the mirror M1 at an angle of 65o to the normal. Find the direction of the ray after it is reflected from mirror M2. • The reflected ray is directed toward the mirror M2. Making an angle of 90o 65o = 25o with the horizontal. • From the triangle made by the first reflection and the two mirrors: 180o 120o 25o = 35o (angle of the first reflected ray with M2. • Therefore, this ray makes an angle of 55o with the normal to M2. • From the law of reflection the second reflected ray makes an angle of 55o with the normal to M2.

19. Example 35.2 Double Reflection (2nd part) • From Example 35.1 if the rays are extended behind the mirrors, they cross at 60o, so that the overall change in direction of the light ray is 120o (same angle between mirrors). If the angle between mirrors is changed, is the overall change in the direction of the light ray always equal to the angle between the mirrors? • NO! By using the law of reflection and the sum of the interior angles of a triangle:  =180o (90o )   = 90o+    . • From the highlighted triangle:  + 2 + 2 (90o ) =180o  = 2(  ) • The change in direction of the light ray is the angle  = 180o    = 180o 2(  )   = 180o 2[  (90o+   )] = 360o 2 •  = 120o  = 120o •  = 90o  = 180o (RETROREFLECTION)

20. Retro-reflection • Assume the angle between two mirrors is 90o • The reflected beam returns to the source parallel to its original path • This phenomenon is called retro-reflection • Applications:

21. 35.5 Refraction of Light • When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the energy is reflected and part enters the second medium • The ray that enters the second medium is bent at the boundary • This bending of the ray is called refraction

22. Refraction, 2 • The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane • The angle of refraction depends upon the material and the angle of incidence (35.3) • v1 is the speed of the light in the first medium and v2 is its speed in the second • The path of the light through the refracting surface is reversible • For example, a ray travels from A to B • If the ray is originated at B, it would follow the line AB to reach point A

23. Quick Quiz 35.2 Following the Reflected and Refracted Rays • Ray  is the incident ray • Ray  is the reflected ray • Ray  is refracted into the Lucite block • Ray  is internally reflected in the block • Ray  is refracted as it enters the air from the block

24. Active Figure 35.10 (SLIDESHOW MODE ONLY)

25. Refraction Details, 1 • Light may refract into a material where its speed is lower • The angle of refractionis less than the angle of incidence • The ray bends towardthe normal

26. Refraction Details, 2 • Light may refract into a material where its speed is higher • The angle of refraction is greater than the angle of incidence • The ray bends away fromthe normal

27. Active Figure 35.11 (SLIDESHOW MODE ONLY)

28. Light in a Medium • The light enters from the left • The light may encounter an electron • The electron may absorb the light, oscillate, and reradiate the light • The absorption and radiation cause the average speed of the light moving through the material to decrease

29. The Index of Refraction • The speed of light in any material is less than its speed in vacuum • The index of refraction, n, of a medium can be defined as (35.4) • For a vacuum, n = 1 • We assume n = 1 for air also • For other media, n > 1 • n is a dimensionless number greater than unity • n is not necessarily an integer

30. Some Indices of Refraction

31. Frequency Between Media • As light travels from one medium to another,its frequency does not change • Both the wave speed and the wavelength do change • The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same

32. Index of Refraction Extended • The frequency stays the same as the wave travels from one medium to the other • So: (35.5) • Since v1≠v2 then 1≠2 • The ratio of the indices of refraction of the two media can be expressed as various ratios (35.6)

33. More About Index of Refraction • Equation (35.6) can be simplified to compare wavelengths and indices: 1n1 = 2n2 • In air, n1» 1 and the index of refraction of any medium can be defined in terms of the wavelengths (35.7) • Since n > 1, then

34. Snell’s Law of Refraction • Now we can rewrite equation (35.3) as (35.8) • 1 is the angle of incidence • 2 is the angle of refraction • The experimental discovery of this relationship is usually credited to Willebrord Snell and is therefore known as Snell’s law of refraction

35. Example 35.3 Angle of Refraction for Glass • Light is refracted into a crown glass slab • 1 = 30.0o, 2 = ? • n1 = 1.00 and n2 = 1.52 • From Table 35.1 • 2 = sin-1(n1 / n2) sin 1 = 19.2o • The ray bends toward the normal, as expected

36. Example 35.4 Laser Light in a Compact Disc • A laser in a CD player generates light that has a wavelength of 780 nm in air. • (A). Find the speed of this light once it enters the plastic of a CD (n = 1.55) • (B). What is the wavelength of this light in the plastic?

37. Material for the Midterm • Examples to Read!!! • Example 35.3(page 1106) • Example 35.6(page 1106) • Homework to be solved in Class!!! • Question: 3 • Problems: 6, 21