Reflection and Refraction Lab Determining the Index of Refraction and Critical Angle PURPOSE: The purpose of this experiment is: 1) to study the two fundamental laws of geometric optics: the laws of reflection and refraction between two optical media (in the present case, air and liquid); 2) to observe the total internal reflection of a ray in the liquid and determine the critical angle for water-air interface; 3) to calculate the index of refraction for water and compare it to the standard value of 1.333. APPARATUS: Diode laser, a circular acrylic tank, water. DESCRIPTION OF APPARATUS: A circular acrylic water tank with a clear front has a white back with a printed protractor. A pivoting arm attached to the back plate can be rotated 360° around the tank and carries a diode laser with a built-in beam spreader (lens). The tank will be half-filled with water, and a bright, narrow ray is directed onto the water surface from above or below to measure the incident and refracted angles. The critical angle and total internal reflection can also be clearly demonstrated. BACKGROUND: Reflection of light from a surface is what allows us to see objects that are not luminous. Different colored objects reflect different colors of light. A mirror is a smooth surface that reflects light in such a way that we can view images of objects. Law of Reflection: The Law of Reflection states that if the incoming light forms an angle of incidence (θi ) with a line normal to the surface, then the light reflected off the surface will form an angle of reflection (θr) with the normal line which is equal to the angle of incidence. This is shown in Figure 1. Refraction occurs when light changes direction as it passes from one medium to another. For example, a straw in a glass of water may appear bent or disjointed at the surface of the water because the direction of propagation of the light changes when traveling between water, glass, and air. Law of Refraction: Snell’s Law states that if the incoming light is traveling in a medium with an index of refraction of n1 and forms an angle of q1 with a line normal to the surface as shown in Figure 2, then the light that enters the second medium of index n2 will form an angle of q2 with the normal line where the refracted angle is given by the equation n 1 sinq1 = n2 sinq2 (1) Snell’s Law predicts that the light will get bent toward the perpendicular line if n1 < n2 (such as for light in air entering glass from air: see Figure 2) and will get bent away from the perpendicular line if n1 > n2 (such as for light in glass entering air). When n1 > n2, sin(q2) in eq. (1) can exceed 1. In this case, no refraction can take place and the ray is completely reflected back into the first medium. This is called total internal reflection, which occurs if the angle q1 is greater than a certain critical angle qc given by the condition sinq2=1. Combining the above condition with eq. (1) we obtain: sinqc=n2/n1 If the second medium is air (whose index of refraction is very close to 1), this angle can be used to check the index of refraction of the first medium: sinqc=1/n1 (2) PROCEDURE: CAUTION: Never look directly into the laser beam: it may damage the retina. Set up the experiment: 1. Place the unit on a flat surface such as a table top. 2. Add water to the tank until it's level reaches the horizontal line on the scale. 3. If the surface of the water does not line up with the horizontal line, adjust the leveling screw(s) at the base to bring them into alignment. MEASUREMENTS: 1. Turn on the laser. 2. Move the laser to the 3rd quadrant (left lower corner) and set the angle of incidence to 200. Record the angles of reflection and refraction in Table 1. Theoretically, the angle of incidence and reflection should be equal. Are they (within experimental error)? 3. Change the angle of incidence to 30o, 40o, 45o. Record the angle of reflection and refraction in your table. Observe the brightness of the reflected rays. Compare the angles of incidence with their corresponding angle of refraction. 4. Continue to increase the angle of incidence while observing the change to the reflected and refracted rays. At a certain point the refracted ray will disappear. The reflection at this point is called total internal reflection. Record the angle of incidence which is called the critical angle. 5. Continue to increase the angle of incidence to 50o,70o, 80o. Record in the table the values of the angle of reflection (no refraction for these angles, so cross out the corresponding cells . Repeat steps 1-5 for the second quadrant (left upper corner). Record your date in Table 2. Note that in this case there is no critical angle and your table will be completely filled. CALCULATIONS: 1. Calculate sin(q1), (q1-q2) and sin(q3). 2. Plot a graph of sin(q3) vs. sin(q1) (Table 1). Don't forget to label your axes and write their units. 3. Determine the slope of the graph and calculate the water refraction index. 4. Compare your water refraction index with the standard value of 1.333. Calculate the percent difference. 5. On the same graph plot the sin(q3) vs. sin(q1) from Table 2. 6. Discuss the two graphs. How are they different? Table 1 (water-air) 01 = incidence 03 = refraction 01-02 sin03 20 30 42° 40 60° 02= reflection 202 30° 400 45 48° 500 60° 70° 80° sin01 0.34 0.50 0.64 0.70 0.74 0,76 45 48 72° 80° 90° 50 60 0.86 70 0.93 0.98 80 Table 2 (air-water) Sle 01 =0 incidence 02 = reflection 03 = refraction sin01 01-02 sin03 20 30 20° 300 40 15 20° 29 40 45 50 50 60 33" 400 45 247 70 70° 80 80 a) complete the tables b) for both sets of data, using your calculator, calculate average and uncertainty for 01-02. c) on the same sheet of paper, plot sin 03 (y axis) Vs. sin 01 (x axis) for both sets of data. d) find the slope in both cases, including units. d) find the intercept in both cases, including units. Discussion: 1) would you say the reflection data are in accord with the law stated above? Explain. 2) Are they precise? YES NO Explain your answer. 2) Are they accurate? YES NO Explain your answer. 3) Indicate possible sources of error. Hint: see the prelab. 4) Are there differences between the reflection data from the two tables? YES NO Explain their possible cause. 5) what is the meaning of the two slopes obtained at point d) above? Write the relevant formulas. 6) how are the two slopes obtained at point d) above related to each other? Write the relevant formula. 7) based on point 6) above, are the two slopes in accord with each other? YES NO Justify your answer.
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