Individual short report (the worksheet)

Pasco Light boxes and power supplies

Semicircular acrylic blocks

Protractors

Rulers/straight edges
 Reflective “triangles” with a straight side, concave side and convex side
Hopefully 30 minutes of data collection (separate from intro and wrapup)
1.
Which one quantity is being measured by at least two different methods in this experiment?
2.
How will you determine which method is most precise and which is most accurate?
3.
The lab does not take into account the dispersion of light through a medium (this means that the index of refraction depends on the frequency of light). How might this affect your results?
4.
Are there lower or upper bounds on the index of refraction for a material?
5.
What is a practical application or use for the total internal reflection?
1.
Which one quantity is being measured by several different methods in this experiment? n, the index of refraction for acrylic, is measured twice in the lab.
2.
How will you determine which method is most precise and which is most accurate?
The n with the smallest uncertainty will be the most precise measurement while the n that is closest to the accepted value for acrylic, 1.49, is the most accurate.
3.
The lab does not take into account the dispersion of light through a medium (this means that the index of refraction depends on the frequency of light). How might this affect your results?
The refracted beam will have a width (blue bends better) – could make measuring the exact angle of refraction difficult.
4.
Are there lower or upper bounds on the index of refraction for a material?
The index of refraction cannot be less than 1 – otherwise the speed of light in a material would be faster than c! Also, as in the previous question, the index depends on the frequency, so the limits would depend on the transmission properties of the material.

5.
What is a practical application or use for the total internal reflection?
Fiber optics, periscopes…etc. etc.

Introduce the equipment here – the main key is that folks need to spend some time looking it over before we start data collection because then we’ll turn off the classroom lights.

Warn students that bags need to be stored (for safety) under the tables and to pay attention to chairs that might be in the middle of the room.

Have students help pull down the shades in the room as well (for the first studio of the day).

The lamp in the light box will get quite warm – warn students to unplug it when they don’t need it and to be careful when handling it.

The first part of the lab is pretty open-ended – don’t prompt them too much – but do give a heads up that it isn’t meant to be a long investigation (i.e., they should be able to answer it all in about 5 minutes).

Suggest all students make their traces with the room lights off but wait to use the protractors to make angle measurements until we turn the lights back on (and emphasize that each section of data collection should take on the order of 5 minutes).

The open investigation may get some students stuck – point out that they have a reflective surface with different curvatures – how can they measure incident and reflection angles? And does it matter which surface they use?

Watch that students don’t spend too much time on the Snell’s law (part 2) – they only have to trace out three different rays.

The third part (TIR) should also be quick, but we do need to watch that they are working at the right interface (don’t immediately tell people). Also, watch to see they are going from the higher index of refraction material (acrylic) to the lower index of refraction
(air).

Hopefully students will be able to measure their angles and immediately determine the index of refraction in class. Perhaps have the students write these values up on the board and compare across the classroom to see the range of values, or on a Google doc

End with a general discussion about indices of refraction and why we care – perhaps use the twisted piece of acrylic demo (spiral and a laser pointer) to show how TIR can be used (like with fiber optics, which is the “backbone” of our modern telecommunications network).

1.
For the drawing below: (a) Find the refractive indices of material A and B. (b) Find the angle

.
2.
The critical angle of a certain material (say, a piece of glass of unknown refractive index n) in air (refractive index of air is 1.0) is 40 0 . What is the critical angle of the same glass if it is immersed in water (refractive index of water is 1.33)?
1.
For the drawing below: (a) Find the refractive indices of material A and B. (b) Find the angle

. a) From the first interface, we have that 𝑛 𝑎𝑖𝑟 sin 40° = 𝑛
𝐴 sin 20° so 𝑛
𝐴
= 1.88
the second interface, we now have
. From 𝑛
𝐴 sin 20° = 𝑛
𝐵 sin 30° , using the value we found for 𝑛
𝐴
we can find that 𝑛
𝐵
= 1.29
b) At the final interface we have 𝑛
𝐵 sin 30° = 𝑛 𝑎𝑖𝑟 found for 𝑛
𝐵 sin 𝜃 , using the value we we find that 𝜃 = 40° So we see the effect that light is shifted laterally, but

emerges with the same angle once it is back in the original material.
2.
The critical angle of a certain material (say, a piece of glass of unknown refractive index n) in air (refractive index of air is 1.0) is 40 0 . What is the critical angle of the same glass if it is immersed in water (refractive index of water is 1.33)?
The critical angle occurs at total internal reflection – when the refracted angle is 90⁰.
This means with air: 𝑛 𝑎𝑖𝑟
Solving, yields 𝜃 𝑐 sin 90° = 𝑛 sin 40° material. Now the glass is immersed in water and we have 𝑛 𝑤𝑎𝑡𝑒𝑟
= 58.7° .
, This means that 𝑛 = 1.56
for this sin 90° = 1.56 sin 𝜃 𝑐
.
Names:_________________________ KEY _________________________ Group:_______________
DATA and DATA ANALYSIS (23 pts)
Part 1: Reflections (6pts)
Describe your experimental setup to test the law of reflection and include your data. Locally, even a curved surface looks like a plane mirror (the Earth is flat, for example, in our close frame of reference). Can verify this by testing different angles with the curved mirrors.
Part 2: Snell’s Law (10pts)
How can you confirm that your optic is set up correctly? (1 pt) –check that angle of incidence =angle of reflection
Angle of Incidence ± Angle of Refraction ± n ± *
45⁰
<45⁰=
>45⁰= show your calculation to determine n. Table needs to be filled in (6 pts plus 3 pts for calculated n’s – showing work somehow – graph or not. (subtract 2 pts for no uncertainities))
Part 3: Internal Reflection (7 pts)
Record any changes in the reflected and transmitted ray as you increase the angle of incidence.
(1 pt – might note some dispersion and difficulty taking the measurement)
Record the critical angle: (2 pts, # and uncertainty) θ C
= ____________± ______________
Calculate the index of refraction (show your work): (4 pts, #, work shown and uncertainity) n=___± ____
Discussion Questions (12 pts)

Compare your results for the index of refraction with the value of 1.49 for acrylic. Which of your measurements is the most precise? Which is the most accurate? Why? Comparison (2pts)
Identifying (correctly for their data) the most precise (1pt) and most accurate (1pt)
Calculate the speed at which light travels inside the acrylic block and compare it to the speed of light in a vacuum. (2 pts) #±# and units and then comparison to c
What is the largest source of error in the experiment? (2 pts) Largest source of error is most likely the thickness of the lines for making angle measurements… or proper alignment for measuring angles.
How would you improve the experiment in the future? (2pts) – Evaluate based on depth of thought and insight.
What did you learn from this lab that could benefit you in the future? (2 pts) – Personal insights

1.
Which one quantity is being measured by at least two different methods in this experiment?
2.
How will you determine which method is most precise and which is most accurate?
3.
The lab does not take into account the dispersion of light through a medium (this means that the index of refraction depends on the frequency of light). How might this affect your results?
4.
Are there lower or upper bounds on the index of refraction for a material?
5.
What is a practical application or use for the total internal reflection?
The Law of Reflection
When a ray of light strikes a plane mirror, the light ray reflects off the mirror and changes its direction of travel. By convention, the direction of a light ray is expressed as the angle the light ray makes with the line normal to the surface. The angle of incidence is the angle between the normal and the incident ray. The Law of Reflection states that the angle of incidence equals the angle of reflection. 𝜽 𝒊
= 𝜽 𝒓
Refraction
Figure 1
When a ray of light strikes the surface of a piece of transparent material, the beam is split — part of the beam is reflected from the surface, while the rest is transmitted into the material. The most common example of refraction is the bending of light when it travels from water to air, which causes submerged objects to appear displaced from their actual positions. Experiment has shown
(and you will verify in this lab) that the angle of the reflected light is equal to the angle of the incident light (both angles are conventionally measured with respect to a line normal to the surface). For the transmitted ray, the path the light takes is bent as it passes from one medium into another. This bending of the light ray is known as refraction . The angle of the refracted ray is related to the angle of the incident ray (see
Fig. 1) by Snell’s Law, also known as the Law of Refraction: n
1 sin

1
 n
2 sin

2
(1) where n
1
and n
2
are the indices of refraction of medium 1 and medium 2, respectively. The index

of refraction of a material is defined to be the ratio of the speed of light in vacuum to the speed of light in the material, n = c /v. The index of refraction of air varies only slightly (<0.03%) from one, and for this experiment is taken to be one, i.e. n air
= 1.
Total Internal Reflection
If light passes from one medium into another medium of smaller n , the angle of refraction will be larger than the angle of incidence. At the critical angle of incidence,
 c
, the angle of refraction will reach 90°. The “transmitted” light is not transmitted into the second medium, but travels along the boundary of the two media, parallel to the surface (see Fig.2). For incident angles greater than the critical angle, all the light is reflected back into the first medium; this condition is known as total internal reflection .
Since the critical angle is the angle for which the refraction angle is 90°, we have sin 
1
= sin 90° =
1. Equation (1) gives:
sin
 c
 n
1 n
2
.
Part 1
– Reflections
Figure 2
(2)
Does the law of reflection apply to curved surfaces like it does to flat surfaces? How can you use the triangular reflective optics piece to answer this question? Give an explanation for the results you observed.
Part 2. Snell’s Law and Index of Refraction
In this part of the experiment you will study the reflection and refraction of light from a plane separating two media (air and acrylic). You will verify that the path of the refracted light satisfies
Snell's law, and as a result, you will determine the index of refraction of acrylic.
1.
Place the semi-circular piece of acrylic in the middle of a sheet of paper. Use a pencil to trace around the perimeter of the component.
2.
Use the light source to shine a single ray of light toward the center of the flat side at a 45 ⁰ incident angle.
3.
Trace the rays going in and coming out of the acrylic.
4.
Remove the acrylic piece and connect the two rays to show the path that light followed while inside the acrylic.
5.
Use the protractor to measure the angle of refraction that the light ray makes with the normal line at the interface and record your values.

6.
Repeat the process for an initial incident angle larger than 45° and then for an initial incident angle smaller than 45°.
Part 3. Internal Reflection
In this part of the experiment, you will observe that light cannot pass from a medium (acrylic disk) into another medium (air) with a lower index of refraction if the angle of incidence is greater than the critical angle, given by Eq. (2). The light is totally reflected back into the medium. You will measure the critical angle of the acrylic and use Eq. (2) to determine its index of refraction.
1.
Send light from the light source towards the circular face of the component. In this way the ray will approach the flat side of the disk from the acrylic side and exit on the side with air (lower index of refraction). (Why is this geometrical arrangement important?)
2.
Starting from a small angle of incidence (near 0°), gradually increase the incident angle by rotating the light source.
3.
As the incident angle approaches the critical angle, the refracted ray will approach the flat side of the disk. Determine the angle when the refracted ray just disappears and record the angle as 𝜃 𝑐
.
4.
Estimate the uncertainty in your measurement of
 c
.
The two parts of the lab allowed you to measure n , the index of refraction for acrylic. Determine n and its associated uncertainty for each section of the lab.
Summarize the index of refraction derived from Parts 2, and 3. Compare your results with the value of 1.49 for the index of refraction for acrylic. Which of your measurements is most precise? Which is most accurate? What is your average value for n ?
In performing Part 2, what difficulties did you encounter in measuring the angle of refraction at large angles of incidence? How would you take this problem into account in the analysis of your data? Are your results consistent with Snell's Law? Explain. If not, to what do you attribute the differences?
In Part 3, describe the changes in the intensities of the reflected and refracted rays as the angle of incidence approached the critical angle.
What is the speed of light in your acrylic?
What did you learn from this lab that may benefit you in the future?
What is the largest source of error in the experiment?
How would you improve the experiment in the future?

The Bending of Light by Refraction
Acrylic Rhomboid Template
45° incident in air
Interface 1 refracted in acrylic incident in acrylic
Interface 2 refracted in air

Names:__________________________________________________ Group:_______________
DATA and DATA ANALYSIS
Part 1: Reflections
Describe your experimental setup to test the law of reflection and include your results.
Part 2: Snell’s Law
How can you confirm that your optic is set up correctly?
45⁰
<45⁰=
Angle of Incidence
>45⁰=
-
Part 3: Internal Reflection
Angle of Refraction ± n ± *
Record any changes in the reflected and transmitted ray as you increase the angle of incidence.
Record the critical angle:
θ C
= ____________± ______________
Calculate the index of refraction (show your work):
n=___________± ______________
Discussion Questions

Compare your results for the index of refraction with the value of 1.49 for acrylic. Which of your measurements is the most precise? Which is the most accurate? Why?
Calculate the speed at which light travels inside the acrylic block and compare it to the speed of light in a vacuum.
What is the largest source of error in the experiment?
How would you improve the experiment in the future?
What did you learn from this lab that may benefit you in the future?
Extra Problems:
For the drawing below: (a) Find the refractive indices of material A and B. (b) Find the angle

.
The critical angle of a certain material (say, a piece of glass of unknown refractive index n) in air
(refractive index of air is 1.0) is 40 0 . What is the critical angle of the same glass if it is immersed in water
(refractive index of water is 1.33)?