Part D: Finding the Speed of Light-with Jello! (25 points) We all know that the speed of light is supposed to be the one stable constant in the universe but few people realize that the speed of light actually depends on the medium it is travelling through. For instance, in water, light is slower than in air. (Just so you don't think Physics has been lying to you: In reality, the speed of light doesn't change but it takes time for the water molecules to absorb the light and then re-emit it over and over and over again.) In this project, you will use Jello (gelatin) and basic laws relating to how light rays behave to calculate the speed of light (in Jello) from basic observations and data. Equipment Required . Laser Clear Jello (gelatin) packet Protractor . Ruler Pencil Graph paper First, you will need to understand the Law of Refraction. This law says that when a light ray passes from one medium into another and is at an angle to the surface of the medium, its path will be refracted (bent) at the boundary. If the ray passes into a MORE dense medium, the ray will be bent toward the normal. If the ray passes into a LESS dense medium, the ray will be bend AWAY from the medium. Second, you will need to understand Snell's Law. Snell's law tells us there exists a relationship between how fast a light ray travels and the angle it makes. Refer to pp. 495-496 in your textbook to review the equation ratios. Snell's law: sin 62 - V2 r Sin 62 n1 sin 01 V 1 sin 01 12 Incident ray Refracted ray If we pass the laser beam from AIR (the first medium) into JELLO the second medium, the light will slow down and bend. Then we can measure both the incident angle " ," and the refracted angle " 02". We know the speed of light in air is essentially the same as the speed of light in a vacuum: Project 1 98 SCIH 036299, 792km/sec or 2.99792x10 m/s. Therefore, we know three of the four variables in this equation and can re-arrange the equation to find that the speed of light in the jello as V2 = V1 sin 62 sin 81 EXAMPLE: You pass a laser beam from air into a thick, clear liquid (corn syrup). The beam hits the liquid with an angle of 30 degrees. The liquid is denser than air so when the beam hits the liquid it bends toward the normal and has an angle of refraction of less than 30 degrees and you measure it to be 20 degrees. What is the speed of light in the corn syrup? Solution: V2 V1 sin 02 _ (2.99792x10 )(sin 20) = 1.99333x10 m/s sin 01 sin 30 Activity Directions: Finding the Speed of Light 1. Mix jello / gelatin as per instructions. It should be clear, with no food coloring or dyes. 2. Pour jello solution into small rectangular container. A small Tupperware container would work well for this. For best results, your jello should be at least 2 cm deep. 3. When the jello has hardened, remove it from the container. If the container is clear, it might be possible to do this project with the jello still in the container instead of removing it. You will need to play around with it to see what works best. 4. Align your laser (this is the hard part...) a. Measure the angle of incidence: Your laser beam needs to hit your jello at a set angle-and you need to know what this angle is. Remember that you measure the angle between the laser beam and the NORMAL, which is a line perpendicular to the surface of the jello. i. You will need to play around with this part to figure out how to secure your laser so it stays in place and how to measure the angle consistently. ii. You will also need to play around with it enough to figure out what it takes to effectively see both where the laser enters the jello and where it exits. b. Measure the angle of refraction: Your laser beam will bend as it passes from air to jello. Measure the angle between the laser beam and the NORMAL as the beam passes through the jello. 5. Using the equation from Snell's law, set up your ratio and calculate v2 (the velocity of light as it passes through the jello. If you want to save some work on the calculator and have reasonable skills with a spreadsheet, you can set up google sheets or excel to make the calculations for you. 6. Repeat this multiple times with different angles until you get consistent results. Project 1 99 SCIH 036Sample Data Table: Note: This is not real data; this data was made up to give you an example of how YOU might set up your experiment and your spreadsheet to calculate these values for you. Trials v, ( m/s ) Angle of sin ( 0,) Angle of sin (02) V 2 = incidence (0,) refraction (02) [V, (sin 2)] / in degrees in degrees ( sin 0, ) 15 degrees 2.99792x108 15 0.6502878402 10 0.5440211109 2.51 x108 (trial 1) 15 degrees 2.99792x108 15 0.6502878402 10 0.5440211109 2.51 * 108 trial 2 15 degrees 2.99792x10 15 0.6502878402 10 0.5440211109 2.51 10 trial 3) 15 degrees 2.99792x108 30 0.9880316241 23 0.8462204042 2.57x10 (trial 1) 30 degrees 2.99792x108 30 0.9880316241 24 0.905578362 2.75x108 (trial 2) 30 degrees 2.99792 x 108 30 0.9880316241 23 0.8462204042 2.57x108 (trial 3) 45 degrees 2.99792x10 45 0.8509035245 37 0.6435381334 2.27x108 (trial 1) 45 degrees 2.99792x10 45 0.8509035245 36 0.9917788534 3.49x108 (trial 2) 45 degrees 2.99792x10 45 0.8509035245 37 (trial 3) 0.6435381334 2.27x108 average = 2.60x108 Examples of excel table formulas V is a constant = 2.99792E8 = 2.99792x10 sin( 8,) formula: =abs(sin(C2)) sin ( 2) formula: =abs(sin(E2)) V2 formula: = (82 * F 2 ) /D2 Caution: if you do not have a good understanding of spreadsheets and how to set up at table with formulas like these, please calculate these values manually. Project 1 100 SCIH 036Experimental Data Table (15 points): YOUR data goes here. If this table does not work for you, please create your own table BUT your data must go in an organized table with headings and units. You need to collect enough consistent data to be confident in your answer. Trials , ( m/s ) Angle of sin ( 0 ,) Angle of sin ( 02 ) V 2 = incidence (0,) refraction (02) [V, (sin @2)] / in degrees in degrees (sin 0,) average = Analysis 1. Qualitative observations: Describe the process of collecting data. What went well, what did you struggle with, what would make the process go better? (5 pts) Project 1 101 SCIH 0362. Write a summary paragraph that answers the questions: What did you ask? What did you do? What did you find? What does it mean? And what would you do next? (5 pts)