# 2/16/2016. Reflection and Refraction WHITEBOARD WHITEBOARD. Chapter 21 Lecture What path did the light follow to reach the wall?

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1 Chapter 21 Lecture What path did the light follow to reach the wall? Reflection and Refraction Represent the path from the laser to the wall with an arrow. Why can t you see the beam of light itself but you can see the spot on the wall? Sprinkle chalk dust along the line of propagation. What are your observations? How would the shadow on the wall would look like with each ray model? (One sketch of each ray model, for each experiment) EXPERIMENT 1 EXPERIMENT 2 We can see objects (even tiny ones such as dust) illuminated by light. The path of light is a straight line from the source of light to the object and then (assuming that the behavior does not change) another straight line of reflected light from the object to our eyes) How would the shadow on the wall would look like with each ray model? 1

2 What How would you see on the wall. Explain using each ray model. EXPERIMENT 3 2

3 Ray model of light Ray diagrams Diagram that represents the travel of light from one location to another, drawn as a straight line and an arrow. Testing experiments show that model 1 is inconsistent with experimental evidence. Model 2 is supported: Each point on an extended light source emits light in many different directions. This light can be represented by multiple rays diverging from that point. Shadows and semi-shadows A sharp shadow is called an umbra. A shadow is a region behind the object where no light reaches. A semi-shadow is called a penumbra. A semi-shadow is a region where some light reaches and some does not. It appears as a fuzzy shadow. 3

4 On a sunny day, a streetlight pole casts a 9.6-m-long shadow on the ground. You have a meter stick that, when held vertical, casts a 0.70-m shadow. Use this information to determine the height of the pole. You place a lit candle several meters from the wall in an otherwise dark room. Between the candle and the wall (and close to the candle), you place a piece of stiff paper (or cardboard) with a small hole in it. Use the ray model of light propagation to predict what you will see on the wall. Pinhole camera Cardboard with a small hole in it is the foundation of the pinhole camera, also called a pin hole camera. It consists of a lightproof box with a very small hole in one wall and a photographic plate or film inside the box on the opposite wall. Before the invention of modern cameras that use lenses, pinhole cameras were used to make photographs. Light is a particle that propagates in straight lines, unless it is reflected or enters a new medium. Pioneered by Isaac Newton in his book Opticks Ray Model of Light Theories of Light Ray Model, Wave Model, Photon Model The Ray Model, although not perfect, explains a great deal of phenomena Reflection, refraction, mirrors, and lenses The Ray Model was the first attempt for scientists to model the behavior of light. 4

5 Light is fast! Really fast! 300,000,000 m/s 1/10 th of a second to go from NY to LA 1 light year = the distance that light travels in one year The speed of light in a vacuum is the speed limit of the universe c = 3x10 8 m/s (speed of light in a vacuum) Ray Model of Light One of the most important components of the Ray Model is the way that objects emit light. In a well-lit room, all objects are visible from every angle. Not only this, but every point on the object is visible from all directions! This is because when objects reflect light, the light rays are so numerous that each point on the surface of the object constantly emits light in all directions. The room is completely filled with light, constantly reflecting off of objects! Many, many rays However, we can only detect the ones that reach our eye! Reflection of light Light from a laser pointer shines on a mirror. In fact, there are so many rays constantly reflecting off of ordinary objects that the Ray Model assumes an essentially infinite number of light rays coming out in all directions. incident ray The Law of Reflection normal reflected ray When the mirror is curved, the normal line is basically just the radius of the mirror. incident ray θ i θ r normal mirror The ray reflects symmetrically across the normal line. The normal line is perpendicular to the surface of the mirror, mirror θ i θ r Think of the mirror as a part of a circle! and touches the point where the ray hits the mirror. reflected ray θ i = θ r 5

6 Reflection of light Law of reflection Incident light: light striking the mirror Normal line: a line perpendicular to the surface where the incident light hits the mirror Angle of incidence: the angle between the incident beam and the normal line Angle of reflection: the angle between the reflected beam and the normal line When a narrow beam of light, represented by one ray, shines on a smooth surface such as a mirror, the angle between the incident ray and the normal line perpendicular to the surface equals the angle between the reflected ray and the normal line. The incident beam, reflected beam, and the normal line are in the same plane. reflection = incidence Two mirrors stand on a table, with their faces forming an angle greater than 90 o. Place an phone on the table in front of mirror 2. Use the rule of reflection to predict how to aim a laser beam so that it hits first mirror 1 and then mirror 2, and finally hits the center of the target. Draw a top view Specular and diffuse reflection On a sunny day, if you look at a house with its lights off, the uncovered windows look almost black but the outside walls do not. How can we explain this difference? 6

7 Red eye effect REFRACTION When a camera flash illuminates the open iris, light reflects from the red blood vessels in the retina on the back of the eye. Some of this reflected light passes back out of the pupil and makes the pupil appear red Pearson Education, Inc. Refraction of light Ever wonder why this happens? At the shore of a lake, you see sunlight reflecting off the water's surface. You also see rocks and sea plants under the surface. To see them, light must have entered the water, reflected off the rocks and plants, returned to the water surface, and then traveled from the surface to your eyes. 7

8 Or this? These and many more phenomena can be understood by learning how light refracts Refract to change direction upon entering a new type of material This is responsible for all sorts of image distortions, and we can use it to our advantage! Every material has an index of refraction Symbol: n The index of refraction of a material is a measure of how slowly light travels in that material. The slower light goes in it, the higher its index of refraction will be! Index of refraction of material n = c v Speed of light in a vacuum Speed of light in the material n = c v Index of refraction of a material actually the ratio of how fast light travels in a vacuum divided by how fast light travels in the material. Some common indexes of refraction Whiteboard Quick Quiz Question! What range of values will n have? What values are impossible for n? Answer: Since c ( m/s) is the fastest possible speed for light to have (unhindered in a vacuum), v will always be less than c. This means that n for any material other than a vacuum must be a number greater tha! More dense materials tend to have a higher index of refraction (slower for light). Whiteboard Question! How fast does light travel in water? n = c v 8

9 Why does light travel slower in matter? When light travels through matter, it is constantly being absorbed and re-emitted by atoms. In general, more dense materials will hinder the speed of light. What do we know so far? When light travels from one medium to another, its frequency does not change (frequency depends on the source) v = λf However, its velocity and wavelength will change proportionally. As a result of this change in speed, it is easily observed that light will also change direction. When light travels from one medium to another, it refracts (changes direction). When light travels from one medium to another, it refracts (changes direction) air glass The ray above refracts twice: once entering the glass and once leaving the glass air To show how light refracts, we first need to know how to draw a normal line at the point where the ray strikes the new medium. A normal line is perpendicular to the surface, and crosses through the point where the ray hits the new material. Concepts of Refraction! If a ray goes from a fast medium into a slow medium, it bends toward the normal. If a ray goes from a slow medium into a fast medium, it bends away from the normal. Example: Normal lines on various surfaces θ i θ i v v v v v v θ r θ r θ refracted < θ incident θ refracted > θ incident 9

10 Concepts of Refraction! A useful analogy! Lower n to higher n. Light bends toward the normal. Higher n to lower n. Light bends away from the normal. When a car travels from the road (fast medium) to mud (slow medium), the tire that hits the mud first will slow down first. When a car travels from mud (slow medium) to the road (fast medium), the tire that hits the road first will speed up first. θ i θ r θ r n1 < n2 n1 > n2 This will cause the car to turn toward the normal (just like light!) This will cause the car to turn away from the normal (just like light!) Whiteboard Showdown Using the concepts of refraction and drawing the normal lines, estimate the complete path of the incoming ray as it enters and as it leaves the given object. A WORD OF CAUTION Refraction of light Light rays will never bend past the normal (see below). We can develop a mathematical relationship between the angle of incidence and the angle of refraction. The ray will always end up on the other side of the normal line. (Or along the normal line if it came in along the normal) 10

11 SNELL S LAW! The math! It s just so beautiful! sinq 1 = sinq 2 Rewriting it like If <, θ 2 < θ 1 = sinq 2 sinq 1 shows the concept If >, θ 2 > θ 1 θ 1 θ 2 This works for slowfast and fast-slow transitions BOTH! Gee, thanks Snell! θ 1 θ 2 θ 1 θ 2 Fast to slow, bends towards Slow to fast, bends away Refractive indexes sinq 1 = sinq 2 θ 1 The angles will always be between 0 and 90 This makes the sine function behave nicely, ranging between 0 and 1. θ 2 Ignore this madness =) Give it a go! air n diamond n Draw and label the complete path of the light ray through the block of diamond You will need to use some geometry here 30 n n sinq 1 = sinq sin30 = 2.417sinq 2 q 2 = sin -1 (sin30 / 2.417) 30 θ 2 12 Alternating interior angles show that 12 is also the incident angle for the second refraction This makes the second refraction just the reverse of the first! 11

12 But wait, there s more! Total internal reflection It doesn t all add up yet! Think about it if light goes from a slow medium to a fast medium At the critical angle of incidence, the refraction angle is 90 o. The refracted ray travels along the water-air interface. θ 1 θ 1 θ 1 If 1 < C, light is totally reflected. θ 2 θ 2 θ 2 There is a fundamental limit on how far we can go before the refracted ray can t bend any further! This is called the critical angle. What really happens when light hits a boundary What really happens when light hits a boundary What really happens when light hits an interface This is why you can see your reflection in a window, but also see light coming through the glass purdy cool, huh 12

13 Light traveling from a more optically dense medium to a less optically dense medium Light traveling from a more optically dense medium to a less optically dense medium (increasing 1) Increasing 1 to the point that light refracts at a 90 ( 1 = C) Total Internal Reflection θ 1 As θ 1 approaches the critical angle, θ 2 approaches 90. θ 2 Substituting into Snell s Law, we get sinq 1 = sinq 2 sinq c = sin90 sinq c = q c = sin -1 The critical angle! This gives ri to some trul beautiful resu 13

14 The index of refraction for diamonds is very high compared to ordinary glass (2.4 vs 1.5) As a result, the critical angle for light to be reflected totally as it travels from diamond to air is small (24 vs 42 for regular glass). Therefore most light is rereflected back from a diamond. This gives the characteristic brilliance to a diamond FIBER OPTICS APPLICATION OF TOTAL INTERNAL REFLECTION Thanks Russell Fiber optics We can understand fiber optics by using total internal reflection. Fiber optic filaments are used in telecommunications to transmit high-speed light-based data and in medicine to see inside the human body during surgery. Draw the reflected and refracted rays below. Indicate angles. air n = 1.00 air n = water n = water n =

15 Pro Tip If you ever get DOMAIN ERROR when you try to calculate the critical angle, it means you have flipped the indices of refraction. You can never take the inverse sine of a number that is not between -1 and 1! Light from a coin at the bottom of a fountain reaches your eye at an angle of 27.0 below the horizontal. Determine at which angle you should look to see the coin. Answer: 42.1 You shine a laser light into the water at an incident angle of 42 relative to the horizontal. Determine the angle of the light in the water relative to the normal line. Answer: 34.0 What is the critical angle for total internal reflection of light going from water (n=1.333) into glass of refractive index 1.56? Answer: Not possible Answer: 45 15

16 A mosquito fish hides from a kingfisher bird at the bottom of a shallow lake, 0.40 m below the surface. A leaf has blown onto the lake and floats above the mosquito fish. How big should the leaf be so the kingfisher cannot see its prey from any location above the water? Answer: C = 45 R = 0.46 m The equation below describes a physical process. Make up a problem for which the equation would provide a solution (Sketch it) 1.33 sin 2 = 1.60 sin 60 : Fiber optics Imagine that you have a long glass block of refractive index 1.56 surrounded by air. Light traveling inside the block hits the top horizontal surface at a 41 o angle. What happens next? The light is totally internally reflected during the first incidence on the upper surface. From there in moves down and to the right and hits the bottom surface at 41 16

17 Prisms Prisms for reflection The refractive index of prism glass is greater for violet light and smaller for red light. Prisms reflect almost 100% of the light incident on them, whereas mirrors reflect somewhat less tha00%. Prisms do not tarnish like mirrors. Prisms can invert an image that is, make it appear upside down. Mirages On a hot day, hot air may hover just above the pavement. This hot air is less dense and has a lower index of refraction than the cooler air above it. When light from the sky passes through air with a gradually changing index of refraction, its path gradually bends, leading us to perceive that the source of light is at a different location than it actually is. Mirages Color of the sky Particle model of light Due to their sizes, atmospheric particles reflect blue light more efficiently than other colors. 17

18 Wave model of light Wave model and refraction Imagine a light wave moving in a less optically dense medium 1 and reaching an interface with a denser medium 2 at a nonzero angle of incidence. 18

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