Snell’s law Equipment: The experiment consist of a laser ray box, optics bench, 2 beakers, 2 circular cartesian coordinate ray trace table, roll of paper towel, hand sanitizer, 2 refraction cups, red desk lamp, acrylic lenses, right angle triangle lense, parallel ray bar lense, meter stick, Laser safety goggles, water, glycerin, and protractor. PRECAUTION!! This experiment uses a laser ray box. Do not let the laser beams or its reflections strike your eyes. Also, watch out for the laser beams from other lab benches! People (sometime) don’t always look before they put the laser ray box on. Be cautious and use your goggles!! 1 Purpose Observe and measure the effects of light transmission and refraction through various substances. 2 2.1 Theory Index Of Refraction You will be observing the effects of light being bent as it enters various mediums. This is defined as refracted light. The refracted light you observe will be propagating through various materials at speeds slower then c. Light waves that propagate through the various materials will slow down and this will cause the beam of light to bend in the material. The angle of bend varies on the index of refraction. Below is a table indicating the index of refraction of various materials. 1 General Physics II Lab: Snells law Medium Vacuum Air Water Acrylic glass Ethyl Alcohol Crown glass Plexiglass Glycerol n 1 1.00029 1.33 1.49 1.36 1.52 1.51 1.4729 Keep in mind the index of refraction of any material varies on temperature, pressure, and the wavelength of the light source. Typically light that is in the 400 nm range will deflect at a higher index of refraction then light that is in the 700 nm range. The table above list the index of refraction those various materials at around 589 nm. 2.2 Snell’s Law In vacuum light is regarded to travel approximately at 2.99 x 108 m/s. Which is defined as c. When light propagates through various materials it will travel at a velocity v less than the speed of light. To calculate the index of refraction of the material that light is passaging through use the ratio of (c/v). The initial velocity is defined as c and the velocity that light is traveling through the material which is v. The index of refraction of the material is given by the relatioship between c and v. n = c/v (1) When light enters from one material to the next it will take a path that is dictated by Snell’s law. The angle of the bend is determined by the index of refraction of the material. Again, the bending of the beam of light in the material is called refraction. Snell’s law states the following. n1 sinθ1 = n2 sinθ2 (2) The n1 indicates the index of refraction and θ1 the angle of the initial beam of light with respect to the normal on the surface of the second medium. The n1 and θ1 are the index of refraction of the material and the angle of light entering into the second medium. (In this case we’re labeling the second medium n2 .) When light rays enters a medium with a higher index of refraction. The ray of light in the higher index of refraction will bend toward normal line on the incident surface. The opposite will occur if the rays of light going from a medium of a higher index to a lower index. That is when n2 > n1 . 2.3 Critcal Angle and Total Internal Reflection At the critical angle all the light at the intersection will bend parallel to the surface. This means none of the light passes to the next medium. Once past critical angle total internal reflection occurs. The ray of light travels from a medium with a high index of refraction to a medium with a lower index of refraction greater then critical angle θc .This occurs when the incident angle is equal or greater than the critical angle. The critical angle is determined by the ratio of initial index of refraction over the final index of refraction. Below are images of critical angle and total internal reflection. Equation 3 represents critcal angle. 2 General Physics II Lab: Snells law sinθc = nf /ni 3 3.1 (3) The Experiments Equipment Arrangement and seeing Refraction On your bench you should see an optical track that has two optical table mounts and a white screen all mounted in one dimension. Mount the laser ray box on top of the outer table mount. The laser ray box can produce one, three, or five laser beams at once. In this part we will use the single beam and three beam output. Set up the laser ray box on top of the outer table mount. Make sure the front of the ray box runs perfectly along the center of the ”NORMAL” line on the round table mount. Place your goggles on and turn on the ray box. Select single beam output. Check the laser beam path and make sure that the laser beam runs straight through the center of the following table mount into the center of the white screen. The beam should be parallel to the ”NORMAL” line of the of the round table mount. Look at the following image. 3.2 Observing Refraction Next mount the rectangular shaped parallel bar on the other round table. Align the parallel bar, so that the beam going through the bar runs through the center of the NORMAL line on the ray table. Make sure that its side runs perfectly parallel to the 0 degree line on the round table mount. 3 General Physics II Lab: Snells law Data: Using the turntable rotate the acrylic glass parallel bar at the following angles below. Calculate the index of refraction at each angle. Also, pick three other incident angles, below 60 degrees. Measure the angles of refraction by looking through the acrylic glass parallel bar and using the small circular scale, then calculate n. Keep in mind that the measurement of refraction angle is not exact. The small circular scale of measurement for refraction are in 5 degree increments, so pick good incident angles. Angle of Incidence 15◦ 22◦ 30◦ Angle of refraction Questions: (1) What starts to occur to the incident beam when you go beyond 60◦ ? (2) Explain what is occurring to the beam inside the parallel bar? (3) Why can your data be off? (4) Is it possible to obtain total internal reflection? 3.3 Observing total internal reflection Remove the parallel bar. Realign the optical ray table as in previous section and set the laser ray box to three beam output. Take the right angle triangle and mount it so that all three beams experience total internal reflection. Explain your observations. Questions: (1) How did you arrange the triangle on the round ray table? (2) What angle did you use and why? 4 General Physics II 3.4 Lab: Snells law Determining the index of refraction of different liquids Note: The beakers, and the 2 refraction cups are labeled, so try not to cross contaminate the fluids! In this part of the experiment we will use the refraction cup. Realign the laser with the ray table and switch the laser ray box to single beam output. Align the refraction cup so that the incident beam is hitting the center of the flat side of the cup. The flat side of the refraction should be perfectly to the normal axis on the ray table. Use the pipette and fill the refraction cup with water all the way to the top. Measure the angles of refraction at the following angles, then using equation 2 you will calculate the index of refraction of water. When you are done with water empty the refraction cup into the correct beaker. Use the second refraction cup labeled glycerin and fill it up with glycerin. Repeat as you have done before. Angle of Incidence 15◦ 22◦ 30◦ 39◦ 50◦ Angle of refraction Questions: (1) How would you calculate the index of refraction if you reverse the direction of the dish so that the incident ray is hitting the curved side of the refraction cup instead of the flat side? 3.5 Critical angle This time you will setup the refraction cup so that the laser beam strikes the curved side of the cup. Fill the refraction cup to the top with water. Center and align the refraction cup so that the beam runs through the center of the refraction cup. Next, increase the angle of the refraction cup so that the refracted ray starts to runs parallel to the straight side. This is critical angle. Compare your experimental results to the theoretical value. You can calculate the theoretical value using equation 3. 5 General Physics II 4 Lab: Snells law Comment Be considerate for your fellow humans and empty the refraction cups out into the proper beakers. Wipe the refraction cups, round table, and the top of the bench dry. Place all the equipment back in proper order. If not your TA will take off points. Cheers! 6
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