Revealing Refractions
Using Snell’s Law to identify materials
This lesson is intended as practice in working with applications of Snell’s Law. For a refresher, visit the Physics Classroom
Background
Light travels fastest in a vacuum (2.99 x 10⁸ m/s!). When light travels through any material, it slows down. As a material increases in density and more molecules get in the way, the speed that light can travel slows down. In the vacuum of outer space, light from the Sun takes about 8 minutes to reach Earth. If light had to travel through water the entire way from the Sun to the Earth, that time would increase to about 11 minutes. If it were traveling through a really dense material, like diamond, it would take 20 minutes.
But light doesn’t just slow down when it enters a new material or medium. If it enters at an angle, it actually ends up bending (or refracting) in a very particular way. Scientist Willebrordus Snellius (yes, his real name) used data to find a relationship describing refraction, and went on to name it after himself: Snell’s Law.
n₁ = refractive index of medium 1; ϴ₁ = angle of incidence (calculated from the normal line); n₂ = refractive index of medium 2; ϴ₂ = angle of refraction (also calculated from the normal line)
This new knowledge was an exciting development, not just for scientists but for anyone needing to identify materials, especially jewelers. Many gems and jewels look similar, but a piece of glass has a very different monetary value than a diamond. Could this new mathematical relationship be harnessed to identify materials, and therefore to test what is counterfeit and what is legitimate?
Imagine this: a jeweler has been approached by a customer who would like to sell some rings, all set with green stones. The customer presents the gems as being two emeralds (expensive!) and one garnet (much cheaper). The jeweler knows these gems could actually be any of the following well-known green stones:
Data and images gathered from https://www.starlanka.com/gemstone-colors/green/
Using refraction data, the jeweler can determine which gems are actually in the rings. In this activity, you will be looking at her data and making a suggestion as to what she should offer her customer based on the stones identified.
Dataset
This data set was gathered through a simulator. You can make your own dataset by going to PHET’s Bending Light simulator. For all data, the wavelength (which determines the color) of light was kept constant at 646 nm, and material 1 was always air with index of refraction value nincidence = 1. Simulations were run varying the angle of incidence between 30° - 80°.
Variables
Gem Sample - This categorical variable references the sample number assigned to each material .
angle of incidence (ϴ₁) - This numerical variable describes the angle at which the light is shone onto a surface. It is measured from the “normal” to the beam of light, NOT from the surface to the beam. Measured in degrees.
angle of refraction (ϴ₂) - This numerical variable describes the angle of the refracted light beam in material 2 (the gem). It is measured from the “normal” to the beam of light, NOT from the surface to the beam. Measured in degrees.
Sin (ϴ₁) - This numerical value is a calculation of the sine of the measured angle of incidence in material 1 (air). It has no unit.
Sin (ϴ₂) - This numerical value is a calculation of the sine of the measured angle of refraction through material 2 (the gem). It has no unit.
Activity
Use the Make a Graph tool to create an angle of incidence vs. angle of refraction graph for each sample by showing ϴ incidence on the X axis, and ϴ refraction on the Y axis. Differentiate between the data from the three different samples by showing Gem Sample as Z.
Include your graph here:
Write a sentence describing if the samples look to be the same material or different, using your data qualitatively as evidence.
Snell’s Law is as follows:
Where ϴ₁ is the angle of incidence and ϴ₂ is the angle of refraction. To find the proper relationship between these variables, we must look at the sine of each angle. Create a new graph with sin(ϴ incidence) on X axis and sin(ϴ refraction) on Y axis. Keep the Z axis variable as your gem samples.
Add regression lines, and group by Z. Include a screenshot of your new graph here:
5. Write out the equation for one of the gemstones below using the equations generated by your data. Make sure to substitute in the actual variables of the graph, and not use “x” and “y” in your equation.
Gem #: ___
6. Recalling that the light is traveling from air (n=1) into the material, what is the index of refraction of the sample you were discussing in #5? Type out any relevant equations you use to solve for this value.
7. Identify each of the gem samples based on your data:
8. Write a sentence or two summarizing what you should tell your customer. Use evidence in your explanation!