Download 22 Snells Law File

Student ___________________________________
Lab Date _______________
Lab # _____
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Snell’s Law and Total Internal Reflection
Materials
Ray box or laser, pencil, protractor, metric ruler, slab of glass, white paper
Purpose
To study Snell’s law of refraction of light and to determine the critical angle at which total
internal reflection occurs
Theory
When light waves pass through a substance, they can be partially absorbed, bounced
(reflected), or bent (refracted) as a result of entering the medium. The law of reflection
states that the angle of incidence is equal to the angle of reflection. When "refraction"
occurs the degree of bending depends on both the composition of the medium and the
wavelength of the incoming light. The refraction (bending) of the beam occurs because the
light slows down in the material, so the index of refraction is found to be the ratio of the
speed of light in a vacuum to the speed of light in a material:
𝑐
𝑛=
𝑣
The relationship between the angle of incidence (incoming light) and the angle of
refraction (degree of bending) is given by the equation: 𝑛1 𝑠𝑖𝑛𝜃1 = 𝑛2 𝑠𝑖𝑛𝜃2
where n1 is the index of refraction for air, n2 is the index of refraction for the second
medium θ1 is the angle of the incidence (the angle that the incoming rays forms with the
normal line), θ2 is the angle of refraction (the angle that the refracted ray forms with the
normal line). This relation is also known as Snell's law.
1
If the ray passes from the denser medium to air, there is an angle of incidence θ2c called the
critical angle, for which the refracted angle in the air is θ1=90o. If light is launched in the
denser medium at an angle θ2c, effectively all of the incident light will be “bouncing” back
and forth within the medium. This is the fundamental principle of how light is guided in an
optical fiber. Using the Snell’s law for this critical angle, we would get:
𝑛2 𝑠𝑖𝑛𝜃2𝑐 = 1 ∙ 𝑠𝑖𝑛90𝑜
from where we get:
1
𝑠𝑖𝑛𝜃2𝑐 = 𝑛
2
or
1
𝜃2𝑐 = 𝑠𝑖𝑛−1 (𝑛 )
2
Procedure
1. Place the glass slab on the paper and trace the slab with the pencil carefully around so
you get an imprint of the glass on the paper. Choose a point on the line and with the
protractor and the ruler build the normal line where the light ray will enter the glass. Place
the glass back on its place. Shine the light so it hits the glass exactly at the point you marked
earlier. Make sure to mark the incoming ray and the point where the light exits the glass.
Remove the glass and connect the entrance point with the exit point. Measure the incident
angle 𝜃1 and the refracted ray 𝜃2 . Use Snell’s law to calculate the index of refraction for the
glass slab.
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2. Repeat the procedure described above for another angle of incidence 𝜃1 . Use Snell’s law
to calculate the index of refraction for the glass slab.
3. Calculate the speed of light inside the glass. Explain what happens.
4. Place the glass slab on the paper and trace with the pencil carefully the slab around so
you get an imprint of the glass on the paper. Now shine the laser beam from the side of the
glass instead. Increase the angle of incidence until the refracted ray in the air begins to
disappear. Make sure you mark the appropriate points and rays and measure the critical
angle. Calculate the critical angle as well using the index of refraction you found above.
Calculate the percent error for the critical angle you found.
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