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Snell's Law Refraction of Light By: Brett Rapponotti and Corrine Yap

Snell's Law Refraction of Light

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Snell's Law Refraction of Light. By: Brett Rapponotti and Corrine Yap. Purpose. To determine the relationship between the angle of incidence and the angle of refraction of a light wave traveling through a medium. The media investigated in this experiment are air to plastic and water. - PowerPoint PPT Presentation

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Page 1: Snell's Law Refraction of Light

Snell's LawRefraction of LightBy: Brett Rapponotti and Corrine Yap

Page 2: Snell's Law Refraction of Light

PurposeTo determine the relationship between

the angle of incidence and the angle of refraction of a light wave traveling through a medium.

The media investigated in this experiment are air to plastic and water.

Page 3: Snell's Law Refraction of Light

Equipment Used

circle, divided into four quadrants, with one quadrant divided into separate ten degree sectors

laser beam

medium (plastic)

other medium, plastic filled with water

Page 4: Snell's Law Refraction of Light

Procedure 1. Begin with the solid glass semicircle and align it with the diameter of the circle,

facing the quadrant divided into 10o sectors.2. Place the laser at the “0o” position and shine it through the glass. It should follow

the diameter perpendicular to the glass. Mark the light on the opposite end of the paper circle.

3. Now place the laser at 10o. Mark the refracted light on the opposite end of the circle after it has gone through the glass medium.

4. Repeat step 3, each time adding 10o, until 90o has been reached.5. Using the protractor, measure the angles of refraction. This is best done by

connecting each point to the center of the circle using a ruler and then measuring the angles from the center.

6. Plot Angle of Refraction vs. Angle of Incidence in LoggerPro.7. Draw semichords from the marked points to the perpendicular diameter, creating

right triangles. Do the same for the original angles, and plot Semichord of Refraction vs. Semicord of Incidence.

8. Determine the relationship between the angles and the semichords and also plot Sine of Angle of Refraction vs. Sine of Angle of Incidence.

9. Repeat the experiment using the hollow plastic semicircle filled with water on a new paper circle; make the same measurements and create corresponding graphs.

Page 5: Snell's Law Refraction of Light

Data

Page 6: Snell's Law Refraction of Light

Graphs

Page 7: Snell's Law Refraction of Light

What Now??The angle of incidence and angle of

refraction do not have a linear relationship, although it may seem that way. So we had to find a different relationship. We decided to draw semichords from the points on the perimeter of the circle to the radii and measure them.

Page 8: Snell's Law Refraction of Light

More Graphs

Page 9: Snell's Law Refraction of Light

Thoughts...How is the semichord related to the

angle, then?

radius

semichord

angle

sin(θ) = semichord/radiusSo.....

Page 10: Snell's Law Refraction of Light

Even More Graphs!

Page 11: Snell's Law Refraction of Light

Mathematical AnalysesSine of angle of refraction = sin(ϴR) ,

Sine of angle of incidence = sin(ϴI)

sin(ϴR) = ksin(ϴI)k = ∆sin(ϴR)/∆sin(ϴI)kglass = 0.6532 (calculated by

LoggerPro)sin(ϴR) = 0.6532sin(ϴI)Sine of angle of refraction = 0.6532*Sine of angle of incidenceHm. Now what could that possibly mean?

Page 12: Snell's Law Refraction of Light

Index of Refractiona dimensionless number that describes

the relationship between the speed of light and the nature of the medium through which it travels.

Index of refraction --> nspeed of light --> cspeed of wave --> vn = c/v

Page 13: Snell's Law Refraction of Light

nair = 1

nplastic = 1.495kplastic (calculated by LoggerPro) = 0.65321/0.6532 = 1.531Taking error into consideration,n = 1/kTherefore,sin(θR) = sin(θI)/n for plastic.

Page 14: Snell's Law Refraction of Light

WATER

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More on Water

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Even More on Water

Page 17: Snell's Law Refraction of Light

Mathematical AnalysisSine of angle of refraction = sin(ϴR) ,

Sine of angle of incidence = sin(ϴI)

sin(ϴR) = ksin(ϴI)k = ∆sin(ϴR)/∆sin(ϴI)kwater = 0.7621 (calculated by

LoggerPro)sin(ϴR) = 0.7621sin(ϴI)Sine of angle of refraction = 0.7621*Sine

of angle of incidence (water)

Page 18: Snell's Law Refraction of Light

Therefore,the same conclusion can be drawn. nwater = 1.33283kwater = 0.76211/0.7621 = 1.312Taking error into consideration, nwater = 1/kwater

So, sin(θR) = sin(θI)/n for water as well.

Page 19: Snell's Law Refraction of Light

But why 1?We can't just say, oh, let's divide one by

the constant because it works out that way! One is a significant number. Remember that

nair = 1, which is also nvacuum.The angle of incidence was measured as

the light wave was traveling through air, while the angle of refraction was measured once the light traveled through a different medium.

Therefore, nair = nmedium of incidence and nplastic or nwater = nmedium of refraction

Page 20: Snell's Law Refraction of Light

WHOA!sin(θR)/nI = sin(θI)/nR

Rearranging,nRsin(θR) = nIsin(θI)

This is Snell's Law!