Properties of Waves

1. Properties of Waves Refraction of Light and Sound Waves

2. Refraction When light bends in going obliquely from one medium to another, we call this process refraction.

3. Refraction • Refraction occurs to minimize the time taken by light to travel from A to B. • Just as if you wanted to save someone from drowning, the quickest path would not be a straight line – it would be the dashed path shown.

4. Refraction Light follows a less inclined path in the glass. • Light travels slower in glass than in air, so it minimizes the time it spends in the glass.

5. Refraction Light rays pass from air into water and water into air. • Pathways are reversible for both reflection and refraction.

6. Index of Refraction Index of refraction, n, of a material • indicates how much the speed of light differs from its speed in a vacuum. • indicates the extent of bending of rays. • ratio of speed of light in a vacuum to the speed in a material.

7. Index of Refraction • The generally accepted speed of light in a vacuum is 3.00 x 108m/s; however, the speed of light varies according to the material that is travelling through. The speed of light in liquids and solids is significantly lessthan in a vacuum. • The ratio of the speed of light in a vacuum (c), to the speed of light in a given material (v), is called the absolute indexof refraction (n) of the material. • n = c.also known asc = nvalso known asv= c. vc= vn n

8. Just by looking at this formula, we can predict: • The unit(s) of the index of refraction: there are none! It’s a ratio • The greater the index of refraction for a given material, the slowerthe speed of light in that substance. • The minimum possible index of refraction of a substance would be 1. An index of refraction less than 1would mean that…

9. Example 1: The speed of light in water is m/s. What is the index of refraction for water?

10. Example 2: The index of refraction for diamond is 2.42. What is the speed of light in diamond?

11. Refraction of light • The change in the speed of light as it passes from one medium into another causes it to bend. • Refraction is the bending of light that takes place at a boundary between two materials having difference indices of refraction.

12. Refraction of light CAREFUL….with reflection, the angle of incidence equaled the angle of reflection. With refraction the same is not true. How can we determine the angle of refraction given the angle of incidence? Let’s do the refraction lab to figure this out!

13. Refraction CHECK YOUR NEIGHBOR Refracted light that bends toward the normal is light that has A. slowed down. • sped up. • nearly been absorbed. • diffracted.

14. Refraction CHECK YOUR ANSWER Refracted light that bends toward the normal is light that has A. slowed down. • sped up. • nearly been absorbed. • diffracted.

15. Refraction CHECK YOUR NEIGHBOR Refracted light that bends away from the normal is light that has A. slowed down. • sped up. • nearly been absorbed. • diffracted.

16. Refraction CHECK YOUR ANSWER Refracted light that bends away from the normal is light that has A. slowed down. • sped up. • nearly been absorbed. • diffracted. Explanation: This question is a consistency check with the question that asks about light bending toward the normal when slowing.

17. Refraction Illusions caused by refraction • Objects submerged in water appear closer to the surface.

18. Refraction Illusions caused by refraction (continued) • Objects such as the Sun seen through air are displaced because of atmospheric refraction.

19. Refraction Illusions caused by refraction (continued) • Atmospheric refraction is the cause of mirages.

20. Refraction CHECK YOUR NEIGHBOR When light travels from one medium to another and changes speed in doing so, we call the process A. reflection. • interference. • dispersion. • refraction.

21. Refraction CHECK YOUR ANSWER When light travels from one medium to another and changes speed in doing so, we call the process A. reflection. • interference. • dispersion. • refraction.

22. dispersion • Newton performed experiments that illustrated the dispersionof sunlight into a spectrumand subsequent recombinationinto white light. • Components of whit light are dispersed in a prism (and in a diffraction grating.)

23. A dispersive medium is one in which different wavelengths of light have slightly different indices of refraction. For example, crown glass is a dispersive medium since the index of refraction for violet light in crown glass is higher than for red light. This is responsible for chromatic aberration.

24. Rainbows Rainbows are a result of dispersion by many drops. • Dispersion of light by a single drop

25. Rainbows • Sunlight incident on two sample raindrops, as shown, emerges from them as dispersed light. • The observer sees the red light from the upper drop and the violet light from the lower drop. • Millions of drops produce the whole spectrum of visible light.

26. Snell’s law • Dutch Mathematician Willebrod Snell (1591 – 1626) determined the exact relationship between the angle of incidence and the angle of refraction.

27. Law of refraction Summarized: • The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant (also known as Snell’s Law). • The incident ray and the refracted ray are on opposite sides of the normal at the point of incidence, and all three are coplanar.

28. Example 1: Light passes from air into water at an angle of incidence of 50 degrees. What is the angle of refraction?

29. Example 2: If the angle of refraction of light in crown glass is 30 degrees, what is the angle of incidence? Index of Refraction for Crown glass = 1.52

30. General form of snell’s law • PROBLEM! This version of Snell’s Law is only valid of the first medium is air. For any two media we must use the General Form of Snell’s Law: n1sinθ1 = n2sinθ2 *This equation works for all cases of refraction!

31. Example 3: Light passes from water to into quartz at an angle of incidence of 30 degrees. What is the angle of refraction? Include a diagram.

32. Example 4: Light passing from flint glass into ethanol refracts at an angle of degrees. What is the angle of incidence? Include a diagram.

33. Assignement: • Snell’s Law Assignment (p.18) • Refraction Problems (p.19)

34. Critical Angle and Total Internal Reflection • At a boundary, an incident ray can undergo partial reflection, or, in certain situations total internal reflection.

35. The critical angleis the angle of incidence for which the angle of refraction is 90. At this angle, the refracted ray glances parallel to the boundary • At any angle of incidence greaterthan the critical angle, total internal reflection occurs. This means that no light passes through the boundary. • Total internal reflection is only possible if light is travelling from a morerefractive medium to a lessrefractive medium. (i.e. n2 < n1)

36. Without total internal reflection, there would be no such thing as fibre optics! YIKES! A world without fibre optics technology would be a world without: • The Internet • Cable TV • medical cameras

37. Example: Determine the critical angle for a crown glass and water boundary.

38. lenses Types of Lenses: Lenses are of two basic types – Convergingand Diverging

39. Converging – thicker in the middle than the ends • Diverging – thinner in the middle than the ends Note: • Incident light rays are refracted twice by a lens; once at each boundary. To simplify matters on ray diagrams, incident rays can be shown to refract at the construction line passing through the optical centre of the lens. For a thin lens this leads to a reasonably close approximation because the lateral displacement is quite small.

40. aberrations • Lens defects are called aberrations. They hinder the quality of the image formed. They can be corrected by using aspheric lenses or by using thin lens combinations that cancel out aberrations.

41. Ray diagrams for lenses • How lens diagrams are different from curved mirror diagrams: • Instead of a Vertex (V), a lens has an optical centre(O) which is located at its geometric centre • A lens has two foci, equidistant on either side of the lens, since light behaves the same way when travelling in either direction (Principle of Reversibity). The two foci, F and F' are called the primaryprincipal focus and the secondaryprincipal focus, respectively. F, sometimes also referred to as the primary focal point, is shown on the right side of a converging lens, and on the left side of a diverging lens, while F', the secondary focal point is shown on the opposite side of each respective lens.

42. Rules for drawing ray diagrams for converging and diverging lenses • (Parenthetical remarks refer specifically to diverging lenses) • An incident ray that is parallel to the principal axis is refracted such that it passes through (or appears to have originated from) the principal focus (F). • An incident ray passing through (or heading toward) the secondary principal focus (F') is refracted such that it travels parallel to the principal axis. • An incident ray passing through the optical centre of the lens continues to travel in a straight line.

43. Examples for converging & diverging lens:

44. Thin lens equation • Lens problems are very similar to those done with curved mirrors. Thin Lens Equation = + Magnification Equation M = = -

45. sign convention: • diis positivefor real images and negativefor virtual images • fis positive for converging lenses, and negativefor diverging lenses.

46. Example 1: • An object is 32.0 cm to the left of a converging lens with a focal length of 8.0 cm. Where is the image located?

47. Example 2: • An object 3.0 cm tall is placed 2.0 cm to the left of a diverging lens with a focal length of 3.5 cm. Where is the image located, and what is its size?