Reflection & Refraction

AIM

The aim is to evaluate the laws of reflection and refraction by direct measurements. We will use a ruler and a protractor to trace the paths of light rays (lasers) through a number of optical devices.

CAUTION! This lab uses lasers.

You will be using a laser. Although the power of the lasers used in the laboratory is small,alllasers are potentially dangerous. Never look directly into the beam. Never point a laser beam at another person. Always think about where the laser beams are going if they leave your immediate area; it is highly recommended to block them from leaving in the first place. Also, you must be aware of reflected laser beams, so be especially careful when placing lenses, prisms, mirrors, etc., in the laser beam. IMPORTANT: DO NOT LOWER YOUR HEAD TO THE LEVEL OF THE LASER TO ALIGN IT. Look down on the beam from above.

ALSO: Position the wooden beamstops at the end of your experiment to block the beams after they have passed through your relevant items.

BACKGROUND

Today we only need to use the two basic relations known as the law of reflection and the law of refraction (the latter is often known as Snell's law).

The Law of Reflection is: The angle of incidence is equal to the angle of reflection. This can be written as₁=₂ where the angles are measured from the normal, as indicated in Figure 1. Note that the bottom line is the flat reflecting surface. The light is coming in from the upper left, bounces off the surface, and leaves to the upper right.

Snell's law is a relationship that explains how light passes from one medium to another. Again, the angles are measured relative to the normal of the surface. If n1 is the index of refraction of medium 1 and n2 is the index of refraction of medium 2, then Snell's law is:

n₁ sin(₁) =n₂ sin(₂)

Notice there is also a reflected ray at the surface; the reflection law tells you it will be at the same angle as the incident ray.

Part 1: Testing The Law of Reflection / Experimental Design

Materials: Laser, Triangular Mirror, PASCO protractor

(The protractor is the white circular platform with angle measurements.)

1. Find the flat side of the triangular mirror (not the two curved sides), and place its edge along the line on the protractor labeled "Component".

2. Before turning on your laser source, set it up so that it is pointing close to the "normal" of your mirror (0^o on the protractor). Remember not to lower your head to the level of the laser at any point in this lab; look down from above.

3. Turn on your laser (single laser beam mode), and align your mirror so that the laser beam is as close to "normal" (0^o) as you can make it. What do you observe to be special about this angle? Do your observations make sense? Why? Comment and explain.

The reflected beam is aligned with an incident ray while shining the laser beam as nearly normally into the mirror.

Since the angle of incidence equals the angle of reflection, it makes sense according to the law of reflection. The angle of reflection is equal to the angle of incidence when both are equal to 0. As a result, they coincide.

4. Design an experiment to test the Law of Reflection (see Figure 1 above). You must have at least 4 separate measurements. Explain your experimental plan before you carry it out. Draw labeled figures if necessary.

Mirror, laser, and PASCO protractor as materials

1. Activate by turning on the laser source.

2. Position the mirror such that it is aligned to the "Component" line on the PASCO protractor, where the incident ray is normal.

3. Aiming the protractor at a specific angle and taking a reflection ray reading. four occasions.

5. Use "Insert Table" to design a data table that will work well for your experimental design. Of course it must also be clear and understandable by anyone who reads the table. Then take your measurements, noting an estimated error for each measurement. (If each error is the same, you can list this somewhere rather than put the error on each individual number.)

Students: Insert Data Table Here, then add measured values

We decided to have 0.75 as a measurement error.

i	r
15	15 0.75
25	25 0.75
35	35 0.75
45	45 0.75

• we didn't notice any errors

6. Decide how to analyze your data to test the validity of the Law of Reflection. Explain and perform your analysis here.

My group plotted the data on a graph, built a trendline, and got the equation with the slope and y-intercept from that.

As m=1, b=0, it is a perfect match, thus that's what we should assume.

• Graph

7. To what accuracy did the Law of Reflection seem to hold? Is this better or worse or about the same as the expected error in your measurements, as noted in step 5? Does your answer to the previous question seem reasonable?

Part 2: Index of Refraction Measurements

Materials: Laser, PASCO protractor, Semicircular Glass, Semicircular Water Dish (Filled)

1) Remove the triangular mirror from the protractor, and replace it with the semicircular glass, flat edge along the "component" line.

2) Use the guidelines on the protractor to ensure that the center of the glass is aligned with the center of the protractor. (Slide it along the 'component' line accordingly.)

3) Send the laser beam onto the flat side of the glass, entering the glass just at the very center of the protractor. It should pass into the glass, and then exit from the curved side of the glass. If you have aligned it properly, it should bend as it goes into the glass, but it should not bend as it comes out of the glass.

4) Do the experiments which allow you to fill in the below table. See Figure 2 and Figure 4 for reference.

REFRACTION EXPERIMENT FOR GLASS:

Incident angle (1)	Refracted Angle (2)	Calculated: sin(2)/sin(1)
15o	8	0.53
30o	17	0.55
45o	26	0.62
60o	32	0.61
75o	37	0.62

5) Explain why and how the average value of the final column should be related to the index of refraction of the glass. Use Snell's Law for evidence. (The index of refraction of air is just about 1.00.)

The Average of sin(1)/sin(2) is 1.58

The index of refraction is determined by n=c/v

6) Show a calculation of the percent error of your average measurement of n_glass. (Your instructor will give you the expected value.)

7) Now do the same experiment for water instead of glass. Don't forget to carefully check step 2, to make sure the center of the semicircle is in the correct location. This should also be where the laser hits the water dish.

REFRACTION EXPERIMENT FOR WATER:

Incident angle (1)	Refracted Angle (2)	Calculated: sin(2)/sin(1)
15o	10	0.67
30o	22
45o	32
60o	40
75o	46

8) Show a calculation of the percent error of your average measurement of n_water. (Your instructor will give you the expected value.)

9) Instead of analyzing each data point on its own, it is much better procedure to look at all the data at once on a graph and use a curve fit. Go back to your refraction experiment for glass and make a graph of the incident angle vs. the refracted angle. Attach the labeled graph here and answer the below question.

10) Why would it be tricky to make a curve fit for this graph? Do you see any way you might proceed?

11) Instead of making a curve fit for your above graph, it's often better to scale your data so that it will make a linear fit when plotted. Look at Snell's Law (the law of refraction) and determine what you might plot on your graph such that it should make a straight line when plotted. (Both axes might need to be adjusted.) Once you see how to proceed, go ahead and make the labeled plot.

12) If you did step 11 properly, you can now do a linear fit to your data. Make this fit and attach your labeled graph, along with the labeled curve fit.

13) Analyze your curve fit. What value can you extract from it? Compare this value to the theoretical value supplied by your instructor with a percent error.

14) Explain why it is better to analyze all your data at once, rather than each data point individually.

Part 3: Total Internal Reflection

Materials: Laser, PASCO protractor, Semicircular Glass

1). Replace the water dish semicircle with the glass semicircle, but now rotate it around so that the laser beam enters the curved side of the glass instead of the flat side.

2) Slide the glass along the component line until the center of the semicircle is at the center of the protractor. This will no longer be where the laser beam *enters* the glass; it should now be where the laser beam *exits* the glass. If it isn't, adjust the relative position of the laser accordingly. (If it is aligned properly, the laser should not bend as it goes through the curved surface, and then it should bend right at the center of the protractor as it leaves the glass semicircle.)

3) Redo the refraction experiment from part 2 (Lab 7), measuring all angles relative to the flat side of the glass. Notice that the incident angle is now inside the glass, and the final refracted angle is now outside the glass. (This is opposite how it was for part 2 (Lab 7).)

REFRACTION EXPERIMENT FOR GLASS (Reversed):

Incident angle (1)	Refracted Angle (2)	Calculated: sin(2)/sin(1)
15o	13	0.87
30o	26	0.87
45o	39	0.89
60o	50	0.88
75o	58	0.87

4) Explain two essential differences between these results and your Part 2 results from Lab 7.

5) If you were not able to measure some of the values in your above table, try to compute what they should have been, theoretically. Explain either your results or the problems you are having with obtaining the theoretical results.

6) You should have noticed that there is a special incident angle where the behavior of the laser beam changes dramatically. It is called a "critical angle". Measure this critical angle the best you can, and explain what happens when it is reached.

7) If all you know is the critical angle, it is possible to find the index of refraction of the glass. Use Snell's Law to determine this relationship, and then use your answer to question 6) to calculate the index of refraction. (Hints: Think about your answer to question 5, and also note that it's impossible for the sine of an angle to be greater than one.)

8) Discuss the accuracy of this way to measure n_glass as compared to the other procedure you used in part 2. Is one more accurate than the other? Why might that be?