The Mathematics of Refraction
Student Extras
Improve your problem-solving skills with problems, answers and solutions from The Calculator Pad.
Flickr PhysicsVisit The Physics Classroom's Flickr Galleries and enjoy a photo overview of the topic of refraction and lenses.
Phun With PhETUse this PhET simulation to explore Snell's law. Change the angles and make measurements using the protractor.
Teacher's Guide
Looking for a lab that coordinates with this page? Try The Unknown n Lab from The Laboratory.
Curriculum CornerPractice makes perfect with this computational activity from The Curriculum Corner.
Treasures from TPFNeed ideas? Need help? Explore The Physics Front's treasure box of catalogued resources on ray optics, including the topic of Snell's Law.
Phun With PhETThis PhET simulation allows students to explore Snell's law. Angles and n values can be changed and a protractor can be used to make measurements.
LivePhoto PhysicsDemonstrate how to find n with this video demonstration of refraction. More videos can be found elsewhere.
Determination of n Values
In a previous part of Lesson 2, we learned about a mathematical equation relating the two angles (angles of incidence and refraction) and the indices of refraction of the two materials on each side of the boundary. The equation is known as the Snell's Law equation and is expressed as follows.
where
ni = index of refraction of the incident medium nr = index of refraction of the refractive medium |
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As with any equation in physics, the Snell's Law equation is valued for its predictive ability. If any three of the four variables in the equation are known, the fourth variable can be predicted if appropriate problem-solving skills are employed. The task of using the equation to solve several varieties of problems was thoroughly discussed in a previous part of this Lesson 2. In a similar manner, the equation can be used to determine the index of refraction of a material if the path of light through the material is known. In this part of Lesson 2, we will investigate the details of this task.
A
common lab performed in a Physics class involves the
determination of the index of refraction of an unknown
material. Typically, a series of transparent objects (glass
and Lucite squares, rectangles and triangles) made of an
unknown material are distributed and the task is assigned to
determine the index of refraction of each unknown material.
Of course, the task of determining the index of refraction
value of an unknown material would be easy if the other
three quantities in the Snell's Law equation are known.
Thus, a line of sight method or a laser beam is used to
determine the path of the light into the material, through
the material and out of the material to the students' eyes.
The diagram depicts a typical path of one such ray through a
square block. Observe that the light encounters two
boundaries - the boundary upon entering the glass and the
boundary upon exiting the glass. The ray of light refracts
at each boundary. By measuring the angles of incidence and
refraction and using the index of refraction of air, the
index of refraction of the unknown material can be found.
Calculations can be performed at each boundary and the
results can be averaged. The data table below represents
sample data for the Index of Refraction Lab; the listed
values correspond to the diagram at the right.
Sample
Data
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value |
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Entering Material |
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Exiting Material |
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Ave. n Value ---> |
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The accompanying work for this lab is as follows:
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ni = 1.00 (from table)
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1.00 * sine(45 deg.) = nr * sine(24 deg.)
0.7071 = 0.4067 * nr
(0.7071)/(0.4067) = nr
1.74 = nr
Second Boundary: Light Ray Exiting Material
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nr = 1.00 (from table)
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ni * sine(24 deg.) = 1.000 * sine(45 deg.)
ni * 0.4067 = 0.7071
ni = (0.7071)/(0.4067)
ni = 1.74
Observe in the data table above the two calculated n values are the same. This should not be a surprise since the unknown material only has one index of refraction value. If different values were obtained, it would be the result of some form of measurement error in the retrieval of data.
This method of determining the index of refraction of an unknown material is one more application of the Snell's Law equation. Test your ability to use the equation in this manner by answering the following questions.
Check
Your Understanding
1. Cal Culator is performing an experiment to determine the index of refraction of an unknown material (in the shape of a 45-45-90 triangle). Cal determines that the light follows the path as shown on the diagram below. Use this path, a protractor, a calculator and Snell's Law to determine the index of refraction of the unknown material.
2. The path of a light ray through an unknown material is shown in the diagram below. Make some measurements and determine the index of refraction of the material.
3. Light traveling through air (n = 1.00) is incident upon a triangular block made of an unknown material. The path of the light through the material is shown in the diagram below. Using a protractor and a calculator, determine the index of refraction of the unknown material.
4. Light traveling through air (n = 1.00) is incident upon a 60-60-60 triangular block (the triangle is equilateral; the sides make 60-degree angles with each other) made of an unknown material. The path of the light through the material is shown in the diagram below. Using a protractor and a calculator, determine the index of refraction of the unknown material.
