VIEWS: 5 PAGES: 40 POSTED ON: 9/22/2011 Public Domain
Refraction What does light do when it changes from one medium to another medium? Introduction to Refraction • Light changes mediums all the time! – Remember: a medium is the substance light travels through. – Example: Light can change mediums by traveling from air into water. • Air is the old medium • Water is the new medium Basics of Refraction • When light changes mediums, it changes its speed! • When light changes its speed it bends. • Refraction = the bending of light as it passes from one medium into another medium. Examples of Refraction Here is a laser passing from air into glass. We would expect that the path of the laser would remain unchanged, but since the laser light enters a new medium (glass), it bends. Examples of Refraction Here is a pencil sitting in a glass of water. We would expect the pencil to appear straight, but since the light bends in the water, the pencil appears distorted. Examples of Refraction Ever tried to catch a fish? We would expect to find the fish exactly where we see them in the water, but since light bends when moving from the water to the air, the fish are not where they appear to be. Refraction Definitions • Since the light is bending when it enters a new medium our goal will be to figure out how much it bends. • To find out how much the light bends we will measure two angles: – Angle of Incidence: the angle the light was at in the old medium. • Denoted by the symbol theta: I the “I” means “Incident” – Angle of Refraction: the angle the light is at in the new medium. • Denoted by the symbol theta: r where the “r” means “refraction” Refraction Definitions • We will measure both angles with respect to the Normal Line. • Normal Line = the line that is perpendicular to the boundary of the two mediums. • For example: in the diagram below, the Normal line is shown in blue. New Medium Old Medium Normal Line Diagram of Refraction •The white space is the old medium. •The box is the new medium. New Medium •A light ray travels from the old medium into the new medium. •The light ray in the old medium is shown by a black arrow. •The light ray in the new medium is Old Medium shown by the black arrow in the new medium. •The blue line represents the NORMAL LINE. How Refraction Works •What happens in the diagram: A light ray travels from the old medium to the new medium. •We would expect the light ray to continue on a straight path through the new medium (shown by red New Medium dotted arrow). •But the light ray doesn’t keep going straight! •It bends! The actual path of the Old Medium light ray is shown by the black arrow in the new medium. •The reason it bends to a new angle is that the light travels at a different speed in the new medium. How Refraction Works How much does the light bend? •In order to find out, we need to measure the angles the light rays r make with the Normal line! New Medium •Angle of incidence: I is in blue •Angle of refraction: r is in red i •It is important to note that in this example diagram, the light ray bent Old Medium towards the Normal Line. •In other cases, the light ray could bend away from the Normal Line. Relationship Between Angles and the Mediums • There is a relationship between the angles the light bends at and the mediums it passes through. • This relationship is called Snell’s Law Snell’s Law Snell’s Law is: ni(sin I) = nr (sin r) n = the Index of Refraction of the medium (this is just a naked number) I = the Angle of Incidence • This is the angle of the light ray in the old medium r = the Angle of Refraction • This is the angle of the light ray in the new medium “sin” = Sine, (pronounced like “sign”) is a calculator operation you can do with the two angles. How to Find the Sine (“sin”) of an Angle Taking the Sine of an angle is a mathematical operation we can do using a calculator. On Calculator: Press the “sin” button, then type in the angle, then press “Enter.” On iPod or Cell Phone: Type in your angle, then press the “sin” button, then press “=.” Practice Finding the Sine of an Angle! • Find (sin 30˚) Answer = 0.50 • Find (sin 90˚) Answer = 1.0 • Find (sin 45˚) Answer = 0.70 Back to Snell’s Law! Snell’s Law is: ni(sin I) = nr (sin r) What does this equation mean? It means that if we know the index of refraction (n) for both mediums, and the angle of incidence (i), we can calculate how much the light will bend in the new medium (r) !!! How to Use Snell’s Law There are two types of refraction problem that you will need to learn how to solve: 1. Using Snell’s Equation to find ni or nr 2. Using Snell’s Equation to find i or r Take notes on the steps to solve each type of problem! Type 1: Finding n The Problem: If light passes from air (n = 1.0) into water with an angle of incidence of 36˚, and bends to an angle of 26.2˚, what is the index of refraction (nr ) of water? Step 0: What are we solving for? We are solving for nr Type 1: Finding n The Problem: If light passes from air (n = 1.0) into water with an angle of incidence of 36˚, and bends to an angle of 26.2˚, what is the index of refraction (nr ) of water? Step 1: Draw a picture of what is happening! 26.2˚ Water nr = ? Air ni = 1.0 36˚ Type 1: Finding n The Problem: If light passes from air (n = 1.0) into water with an angle of incidence of 36˚, and bends to an angle of 26.2˚, what is the index of refraction (nr ) of water? Step 2: Write out the Snell’s Law equation. ni(sin I) = nr (sin r) Type 1: Finding n The Problem: If light passes from air (n = 1.0) into water with an angle of incidence of 36˚, and bends to an angle of 26.2˚, what is the index of refraction of water? Step 3: List out what you know from the problem. ni = 1.0 i = 36˚ nr = ? r = 26.2˚ Type 1: Finding n The Problem: If light passes from air (n = 1.0) into water with an angle of incidence of 36˚, and bends to an angle of 26.2˚, what is the index of refraction of water? Step 4: Fill in the Snell’s Law Equation ni(sin I) = nr (sin r) (1.0)(sin 36˚) = nr (sin 26.2˚) Type 1: Finding n The Problem: If light passes from air (n = 1.0) into water with an angle of incidence of 36˚, and bends to an angle of 26.2˚, what is the index of refraction of water? Step 5: Solve the equation for n! To get nr by itself, we will divide both sides of the equation by (sin 26.2˚) (1.0)(sin 36˚) = nr (sin 26.2˚) (sin 26.2˚) (sin 26.2˚) Type 1: Finding n The Problem: If light passes from air (n = 1.0) into water with an angle of incidence of 36˚, and bends to an angle of 26.2˚, what is the index of refraction of water? Step 5: Solve the equation for n! The (sin 26.2˚) will be canceled out on the right side, leaving nr by itself. (1.0)(sin 36˚) = nr (sin 26.2˚) (sin 26.2˚) (sin 26.2˚) Type 1: Finding n The Problem: If light passes from air (n = 1.0) into water with an angle of incidence of 36˚, and bends to an angle of 26.2˚, what is the index of refraction of water? Step 5: Solve the equation for n! Now all we have to do is plug the left side of this equation into our calculator. Try it on your own! Don’t forget to include parentheses!!!! (1.0)(sin 36˚) = nr (sin 26.2˚) You should find that nr = 1.33 Problem Solved!! nr = 1.33 Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction (r)in sapphire? Step 0: What are we solving for? We are solving for r Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction (r)in sapphire? Step 1: Draw a picture of what’s happening in the problem! r = ? Sapphire n = 1.77 Air n = 1.0 ˚ Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction in sapphire? Step 2: Write out the Snell’s Law Equation. ni(sin I) = nr (sin r) Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction in sapphire? Step 3: List out what you know. ni = 1.0 i = 26˚ nr = 1.77 r = ? Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction in sapphire? Step 4: Fill in the Snell’s Law equation. (1.0)(sin 26˚) = (1.77)(sin r) Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction in sapphire? Step 5: Solve for (sin r). To get (sin r) by itself, divide both sides by 1.77. (1.0)(sin 26˚) = (1.77)(sin r) (1.77) (1.77) Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction in sapphire? Step 5: Solve for (sin r). The 1.77 will cancel out from the right side of the equation. (1.0)(sin 26˚) = (1.77)(sin r) (1.77) (1.77) Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction in sapphire? Step 5: Now we are left with: (1.0)(sin 26˚) = (sin r) (1.77) Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction in sapphire? Step 5: Plug this into your calculator to find (sin r): (1.0)(sin 26˚) = (sin r) (1.77) You should find that (sin r) = 0.247 Type 2: Finding The Problem: A light ray passes from air (n = 1.0) at an angle of incidence of 26˚, into a sapphire (n = 1.77). What is the angle of refraction in sapphire? Step 6: Right now we’ve got (sin r). We need to find what r is. Use the inverse sine button “sin-1” to cancel out the sin and find out what r is. sin-1 (0.247) = ________ You should find that r = 14.33˚ Problem Solved!! r = 14.33˚ What is Refraction Good For? Lots of things! For example: Rainbows work by refracting sunlight through water drops. For more details ask Miss Byrne for her Rainbow workshop! What is Refraction Good For? Another example: Fiber Optics are clear cables used to transfer data! These cables revolutionized phone lines and high speed internet! For more details ask Miss Byrne for her Fiber Optics workshop! Now You Try! You are now ready to finish Homework 10 and Homework 11! Use these slides and the notes you took from them to help you solve the homework problems.