Unit 4 Wave Theory of Light. Wave Behaviour

Transcription

1 Lesson43b.notebook February 06, 2014 Unit 4 Wave Theory of Light Wave Behaviour Today's goal: I can explain wave behaviour with; barriers, different mediums, etc... and explain how they relate to real world applications. Point Source

2 Lesson43b.notebook February 06, 2014 Two Point Sources Plane Wave

3 Lesson43b.notebook February 06, 2014 Single Slit Double Slit

4 Lesson43b.notebook February 06, 2014 Obstacle Half a Plane

5 Lesson43b.notebook February 06, 2014 Parabolic Mirror Change in Medium

6 Lesson43b.notebook February 06, 2014 Refraction Snell's Law As a review of Snell's Law, complete the chart using the applet from the website: Use the applet to complete the following table. The values of 1 nand n 2 must be entered manually using the provided values. The values of sinθ can be found in the bottom left of the display. You will need to use a calculator for the last two columns. n 1 n 2 sinθ1 sinθ2 n 1 x sinθ1 n 2 x sinθ

7 Lesson43b.notebook February 06, 2014 Based on your investigation, answer the following: 1) What is Snell's Law? (Equation) 2) Explain in your own words what Snell's Law means. Describe what happens. Use diagrams to help with your explanation. 3) When does total internal reflection occur? (HINT: What is the value of sinθ2 when it occurs?) Try the following examples. Example: Find the angle of refraction for light travelling from air (n = 1.0) to diamond (n = 2.42) if the angle of incidence in air is 20 degrees. Example: Calculate the index of refraction for a substance where the angle of incidence is 30 degrees, the angle of refraction is 50 degrees and the index of the second substance is 1.5. Example: Determine the critical angle (the angle when total internal reflection occurs) for the both the examples above.

8 Lesson44.notebook September 17, 2013 Unit 4 Wave Nature of Light Corpuscular Theory vs. Wave Theory (or Newton vs. Everyone else!) Today's goal: I can explain and identify where past physicists debated over the wave nature of light. How does Light travel? The Greeks (Plato) thought light consisted of "streamers" that the eye emitted and when the streamer struck an object sight was achieved. Later the Greeks (Pythagoras) believed that light travelled as a stream of fast moving particles. Other Greeks (Empedocles) taught that light travelled as a wave like disturbance. Finally the controversy reached a head and in the 17th century two camps had formed: Newton and the Particle Theory (Corpuscular Theory) and company which included French physicist LaPlace. vs. Christiaan Huygens and the Wave Theory and company whichy included Robert Hooke, President of the Royal Society. The Debate Particle vs. Wave Rectilinear Propagation Shadows are created because light travels in straight lines Waves Particles

9 Lesson44.notebook September 17, 2013 Diffraction Light bends when it passes through an aperture. Waves Particles Reflection Light will "bounce" off a surface. Waves Particles

10 Lesson44.notebook September 17, 2013 Refraction Light bends when going from one medium to another. Waves Particles Partial reflection Partial refraction Some light passes from one medium to another, some is "bounced" off a surface. Waves Particles

11 Lesson44.notebook September 17, 2013 Dispersion Different colours in the light spectrum bend differently passing through a medium and in creates the spectrum. Waves Particles Medium Light travels from sources, on Earth and from the Sun. Waves Particles

12 Lesson44.notebook September 17, 2013 The Evolution of Light Christian Huygens passes away (as well as Newton) never knowing the fac that all his research and theories were correct 200 C.E C.E. Light is argued to be either particle or Wave 1600 C.E C.E. Physicists go along with Newton although there is some "shaky" concepts that make progress in research difficult. Some believe or use the "duality" o light to help make progress in their fields' of research C.E. Present James Maxwell arrives! Thank you James Maxwell ( )! The electromagnet wave now allows Wave Theory of Light to explain all aspects of "How does light travel?".

13 lesson45.notebook September 17, 2013 Wave Theory Today's goal: I can explain how wave theory is extended to the concept of the nature of light. A wave is a vibrational disturbance that transfers energy from one location to another. There are 3 categories of waves: Mechanical waves Governed by Newton's laws. They require a medium in which to travel. Examples include water and sound waves, musical instruments, etc... Electromagnetic waves Waves can travel with or without a medium. Waves travel at 3 x 10 9 m/s in a vacuum. Examples include radio, ultraviolet, infrared, etc... Matter waves A combination of particle and wave theories of energy and matter. Particles can behave like waves (wide use in technology) Quantum mechanics!! Types of Waves Transverse Waves Longitudinal Waves

14 lesson45.notebook September 17, 2013 The Transverse Wave and its Properties Wave Concepts Electromagnetic Theory We have discussed Maxwell's model of the electromagnetic wave: There are five properties associated with them: 1) Electromagnetic waves are comprised of oscillating electric and magnetic fields. 2) The electric and magnetic fields are perpendicular to each other. 3) The vibration of electric and magnetic fields are perpendicular to the direction of travel of the wave. 4) The electric and magnetic fields vary sinusoidally in phase with each othe 5) Electromagnetic waves travel at 'c', the speed of light in a vacuum. In other mediums they travel at different speeds which causes refraction.

15 lesson45.notebook September 17, 2013 The Speed of Light Electromagnetic waves are still governed by the universal wave equation: The Electromagnetic Spectrum Radio Microwave Infrared Visible Ultraviolet X Ray Gamma Building Grain of sugar Single cell Bacteria Molecules Atoms Atomic organisms Nuclei Electromagnetic waves can have information encoded in two methods: Amplitude Modulation (AM) or Frequency Modulation (FM) From kinematics we know uniform velocity is calculated by: If we make the following substitutions for one wavelength of light: λ = Δd and T = Δt, then we get: The speed of light is a constant for all electromagnetic waves: 3 x 10 8 m/s

16 lesson45.notebook September 17, 2013 Example: If the radius of Earth is 6.4 x 10 6 m, compare the travel time if you were in a car travelling at the speed of light versus a car travelling at a average speed of 100 km/h. Example: It is 1.49 x m from the Earth to the Sun. Determine how long it takes for light from the Sun to reach Earth.

17 lesson45.notebook September 17, 2013 Phase Shift Rectilinear Propagation Side View End View Point Source Larger Source

18 lesson45.notebook September 17, 2013 Pinhole Camera Reflection Types of Rays: Parallel Diverging Converging Incident versus Reflected Ray

19 lesson45.notebook September 17, 2013 Images in Plane Mirrors Straight on: Object at an angle: Rear view Mirror in Car (silver backing): Day Position: Night Position:

20 lesson45.notebook September 17, 2013 Spherical: Curved Mirrors Parabolic: Homework: Handout Pick and choose for understanding

21 Lesson46.notebook September 17, 2013 Refraction in Light Today's goal: I can explain how refraction applies to light and extend it to Young's Double Slit experiment. Snell's Law: n 1 sinθ1 = n 2 sinθ2 Where: Refractive Index: n = c / v What is refraction? Example: Determine the velocity of light in water in the refractive index is Example: Find the angle of refraction for light travelling from diamond (n = 2.42) to air (n = 1.0) if the angle of incidence is 35 degrees. Determine the critical angle.

22 Lesson46.notebook September 17, 2013 Young's Double Slit Equations Review Wave Properties Large Single Opening Small Single Opening Long Wavelength Small Single Opening Short Wavelength Two Source Interference

23 Lesson46.notebook September 17, 2013 Young's Double Slit Experiment A light source passed through a double slit filter and was viewed on a screen. Top view: The math... For constructive interference to occur:

24 Lesson46.notebook September 17, 2013 Equations: Constructive Interference Destructive Interference Now...

25 Lesson46.notebook September 17, 2013 And then... Finally... The characteristic of double slit patterns is the equal spacing between the bands. The distance between any two consecutive bands can be obtained by: If m is a given order then m + 1 is the next order, mλ = dx m / L

26 Lesson46.notebook September 17, 2013 Example: Two identical sources 5 cm apart operate at 10 Hz. A point on the first nodal line is 10 cm from one source and 11 cm from the other. Determine: A) The wavelength of the waves. B) The velocity of the waves. Example: A source with wavelength 4.5 x 10 7 m illuminates two slits 3.0 x 10 6 m apart. Determine: A) The angle at which the second order maximum occurs. B) The distance the second order maximum is from the centre line.

27 Lesson46.notebook September 17, 2013 Example: Find the spacing between bands for red light (λ = 6.5 x 10 7 ) passing through slits 6 x 10 6 m apart on a screen 1.5 metres away. Homework: pg 527 #44 48 pg 579 #23, 26 33

28 Lesson47.notebook February 20, 2014 Polarization Today's goal: I can explain the concept of polarization and apply it to real world applications, including appropriate calculations. Thanks to Maxwell we know light travels as an electromagnetic transverse wave. transverse wave is a wave that vibrates perpendicular to the direction of travel. Fo example: However, light is not a single wave that travels from the source. Light is comprise of an infinite number of transverse waves vibrating perpendicular to the direction o travel. If we sketch only the electric wave field it looks like this: Definitions: Unpolarized Light: A wave that vibrates in all directions, perpendicular to the direction of travel. Polarized Light: A wave that vibrates only in one direction, perpendicular to the direction of travel. How do we create "polarized light"? Filters, called "Polaroids", allow light wave vibrating in a specific direction to pass through. By removing electro magnetic waves from passing through a Polaroid w reduce the intensity.

29 Lesson47.notebook February 20, 2014 A Polaroid is a trade marked name for an object created by Edwin Land in the 1930's. It is a sheet of plastic embedded with tiny crystals of an iodine compound aligned in regular rows similar to a picket fence. A light passes through the polarizing material some of the electric field waves are absorbed. The other components of light pass through unhindered. Unpolarized light that passes through one Polaroid not only gets polarized in that direction, but it also loses some of its intensity. Thus Now if polarized light passes through a second Polaroid the orientation is important. If it is 90 degrees to the first Polaroid, no light will pass through. However, if it is any angle between 0 and 90, the intensity will vary. Thus

30 Lesson47.notebook February 20, 2014 Example: If two Polaroids are crossed with an angle of 50 degrees between their polarizing directions, what percentage of light is transmitted? Polarizing by Reflection Partial polarization also occurs when light reflects off shiny surfaces. After reflection, the component of the electric field parallel to the surface is unchanged. The other component is partially absorbed, causing light to become partially polarized. For example: Unpolarized Incident ray

31 Lesson47.notebook February 20, % polarization can occur with reflection. The angle this occurs at is called Brewster's angle which is calculated by: tanθb = n 2 / n 1 Example: Calculate the angle at which all of the reflected light is 100% polarized i light reflects out of glass (n = 1.5) to water (n = 1.33). Applications of Polarization Homework: page 527 #51 62

32 Lesson48.notebook September 17, 2013 Thin Film Interference Today's goal: I can explain the concept of thin film interference and apply it to rea world applications, including the appropriate calculations. Everyone at some point in time has witnessed thin film interference. It occurs whe you see the colour spectrum in gasoline or oil that has been spilled or in a soap bubble. This effect occurs due to optical interference. Consider a horizontal film like a soap bubble that is extremely thin, compared to th wavelength of light directed at it from above. Some is reflected Some is refracted The result or transmitted Air film Air Air film Air Air film Air Some examples of reflected light:

33 Lesson48.notebook September 17, 2013 Examples of transmitted light: Properties of Reflected Waves Fixed end (Less dense medium to more dense medium) Free end (More dense medium to less dense medium)

34 Lesson48.notebook September 17, Cases for Thin Film Interference Reflected Light Remember: Transmitted light waves are always in phase from the source. Comparing film thickness (t) to the wavelength of light (λ) For t << λ For t = λ/4 For t = λ/2 Air film Air Air film Air Air film Air Summary: Constructive interference occurs when: Destructive interference occurs when:

35 Lesson48.notebook September 17, Cases for Thin Film Interference Transmitted Light Remember: Transmitted light waves are always in phase from the source. Comparing film thickness (t) to the wavelength of light (λ) For t << λ For t = λ/4 For t = λ/2 Air film Air Air film Air Air film Air Summary: Constructive interference occurs when: Destructive interference occurs when:

36 Lesson48.notebook September 17, 2013 Equations for Thin Film Interference From v = fλ, we know v is the speed of light (Unit is about light waves) So, c = fλ. If we assume the initial equation is the velocity of light in a different medium then we can take a ratio of c / v: Example: In the summer, the amount of solar energy entering a house needs to be minimized. We do this by applying a thin film coating to maximize the reflection of light. If light (assume λ = 568 nm) travels into an energy efficient window, what thickness of the added coating (n = 1.4) is needed to maximize reflected light? Homework: page 580 # 38 42

37 Lesson49.notebook February 21, 2014 Interference in an Air Wedge and Single Slit Interference Today's goal: I can determine the interference patterns that develop from air wedge and single slit screen. t x 1 x2 L Example: An air wedge made of 2 glass slides, 11 cm long, are separated at one end by a piece of paper (t = mm). Answer the following: A) If red light (λ = 663 nm) is shone on the wedge, what is the spacing in the interference pattern between the dark fringes? B) How would the spacing change if the wedge was filled with water (n = 1.33)?

38 Lesson49.notebook February 21, 2014 Diffraction A Review Huygen's Principle Huygen's Principle states that every point on a wave front can be considered as a point source of tiny secondary wavelets that spread out in front of the wave at the same speed as the wave itself. The surface envelope, tangent to all the wavelets, constitutes the new wave front. Circular Wave FrontStraight Wave Front

39 Lesson49.notebook February 21, 2014 Diffraction Through a Single Slit Light that passes through a single, narrow slit is diffracted. Think of a dark night in your house. If one room has a light on and the door to that room is open by a crac what light pattern do you see? The Single Slit Diffraction is similar to the double slit except: 1) The dark and bright bands are not equally spaced. 2) The intensity of the bright bands is not equal. Example: Different cases for single slit diffraction: 1) θ = 0 2) θ 0, ΔL = λ

40 Lesson49.notebook February 21, ) θ 0, ΔL = 3λ / 2 4) θ 0, ΔL = 2λ For constructive interference (Bright lines) For destructive interference (Dark lines)

41 Lesson49.notebook February 21, 2014 Some theoretical mathematics: For right angle triangles that have adjacent sides that are significantly larger than their opposites (like our single slit and screen) we find that... We use this "approximation" and return to our previous equation: sinθ = λ / w and... Example: A slit with a width of 2 x 10 5 m is illuminated by red light of wavelength 620 nm. At what angle does the: A) Third order minimum occur? B) Third order maximum occur?

42 Lesson49.notebook February 21, 2014 Example: Light from a laser has a wavelength of 670 nm. If it passes through a sl with a width of 12 μm and projects on a screen 30 cm away, answer the following: A) How wide is the central maximum i) in degrees ii) in metres B) What is the separation of adjacent minima (excluding the pair on either side of the central maximum)? Homework: Handout Page 581 # 46 53

43 Lesson50.notebook September 17, 2013 Diffraction Gratings Today's goal: I can determine the pattern that develops with diffraction gratings an apply them to real world situations. A diffraction grating is a device used for wave analysis. It consists of a large number of equally spaced parallel slits, which act as individual sources of light. For example: Equations involved for diffraction grating: d = w / N mλ = dsinθ In terms of intensity: Relative Intensity 2 slits 6 slits slits

44 Lesson50.notebook September 17, 2013 Example: Determine the angular position of the first order maxima for violet light (450 nm) when using a diffraction grating with 5400 slits over 3 cm. Example: Which maximum occurs closest to the central axis if the diffraction grating used has lines in 2.5 cm: A) Second order red (730 nm) maximum B) Third order violet (400 nm) maximum C) Second order green (510 nm) maximum Homework: page 582 #55 60