Index of Refraction, Snell's Law, and Brewster's Angle

In summary, the conversation discusses using Snell's law to find the index of refraction for a lab bench. The height and distance were measured, and an angle of 50.9 degrees was calculated. The conversation also mentions the possibility of a refractive index less than 1, but this is unlikely. The conversation ends with the partners double checking their work before submitting their report.
  • #1
alibert0914
2
0

Homework Statement



This was for a lab experiment, and I'm still not sure how this all fits together. We were supposed to use snell's law to find the index of refraction for the lab bench. We measured from the top of the bench to our eye level, and to the center of the bright spot seen through a polaraizer. Height was 0.741 m, and distance was 0.605 m. We used the ref. index of air for n1.


Homework Equations



tan (theta): height/distance

n1sin(theta1) = n2sin(theta2)

thetaB = arctan n2/n1


The Attempt at a Solution



We calculated an angle to be 50.9 degrees. We assumed this to be thetaB, and plugged it in. However, since we were using n1=1 for air, it just seems like a lot of back and forth, and we basically get arctan (thetaB) = n2= 1.23. Most everyone else in the lab seems to have gotten n2 to be less than one. If someone could give us a nudge in the right direction that would be very helpful. Thanks a lot!
 
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  • #2
An index of refraction less than 1.0 is rather unlikely I would think.
 
  • #3
Welcome to PF alibert0914!

I don't think you really need the equation for Snell's law, since refraction is not happening here (EDIT: for the polarization of interest, anyway). If memory serves, the Brewster angle is the angle at which light (with a specific polarization) that is incident upon an interface between two media will be totally reflected (i.e. none of it will be transmitted from the first medium to the second). Since the angle of incidence equals the angle of reflection, the angle you measured was equal to the angle of incidence. So you have

tan(θB) = n2/n1 = n2

= height/distance = 1.22

As for your classmates -- a refractive index less than 1? I think not. This would mean that the speed of light in the lab bench material would be faster than c, the speed of light in a vacuum.
 
  • #4
Thanks so much everyone! My partner and I just wanted to double check everything before we turn our report in. :biggrin:
 
  • #5


I can understand how this may be confusing. Let's break down the concepts of index of refraction, Snell's law, and Brewster's angle to better understand their relationship and how they apply to your lab experiment.

The index of refraction (n) is a measure of how much a material can bend light. It is a ratio of the speed of light in a vacuum to the speed of light in the material. Different materials have different indexes of refraction, which can affect how light travels through them.

Snell's law is a formula that relates the angles of incidence and refraction when light passes through two different materials with different indexes of refraction. It is represented by the equation n1sin(theta1) = n2sin(theta2), where n1 and n2 are the indexes of refraction of the two materials, and theta1 and theta2 are the angles of incidence and refraction, respectively.

Brewster's angle is a specific angle at which light is polarized when it reflects off a surface. It is represented by the equation thetaB = arctan (n2/n1), where n1 is the index of refraction of the first material, and n2 is the index of refraction of the second material.

In your lab experiment, you were using Snell's law to find the index of refraction of the lab bench. The angle you calculated (50.9 degrees) is the angle of incidence (theta1) when light passes from air (n1=1) into the lab bench (n2). However, in order to solve for n2, you would need to know the angle of refraction (theta2) as well.

It is possible that other students in your lab may have measured the angle of refraction instead of the angle of incidence. This would explain why their calculated index of refraction for the lab bench is less than 1. Another possibility is that there may have been some error in your measurements or calculations.

In order to get a more accurate result, you could try repeating the experiment and making sure to measure both the angle of incidence and the angle of refraction. You could also try using different materials with known indexes of refraction to compare your results to.

Overall, the concepts of index of refraction, Snell's law, and Brewster's angle are all related and can be used to understand and predict the behavior of light as it passes through different
 

1. What is the index of refraction?

The index of refraction is a measure of how much a material can bend light as it passes through it. It is calculated by dividing the speed of light in a vacuum by the speed of light in the material.

2. What is Snell's law?

Snell's law, also known as the law of refraction, is a formula that describes the relationship between the angle of incidence and the angle of refraction when light passes through a boundary between two different materials. It is written as n1sinθ1 = n2sinθ2, where n1 and n2 are the indices of refraction for the two materials and θ1 and θ2 are the angles of incidence and refraction, respectively.

3. How does the index of refraction affect the speed of light?

The index of refraction is inversely proportional to the speed of light in a material. This means that the higher the index of refraction, the slower the speed of light will be in that material.

4. What is Brewster's angle?

Brewster's angle is the angle of incidence at which light with a certain polarization will be completely reflected off a surface. This angle is related to the indices of refraction of the two materials in contact and can be calculated using the formula tanθB = n2/n1, where n1 and n2 are the indices of refraction for the two materials.

5. How is the index of refraction related to the density of a material?

The index of refraction is directly proportional to the density of a material. This means that as the density of a material increases, so does its index of refraction.

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