Hanne Martine G. Ræstad
1.j Physics
25.03.2014
Snell’s Law Verification of Snell Snell’s ’s Law of Refraction
Apparatus glass slab pins
compass ruler
graph sheet
cork board
pencil eyesight
Theory When a light ray passes from one medium to another, its velocity changes with respect to the difference in refractive indices of the two media. Snell’s law states that the ratio of the sine of the angle of incidence ( to the sine of angle of refraction ( will be equal to the ratio of refractive indices of the second media to the first. ( )
The refractive index of a substance ( ) is defined as the ratio of velocity of light in vacuum ( ) to the velocity of light in the medium ( ).
Procedure The goal of the experiment itself was to find and note the refractive angles corresponding to various angles o f incidence, so that we can use these to later verify Snell’s law of refraction. We first began with a sheet of graph paper which was to be used to record our findings. We drew a coordinate system approximately in the middle of the paper and proceeded to draw a circle of radius 10 centimetres with its centre in the point of origin using the compass. The graph paper was then placed on the cork board. The glass slab was placed so that one of the edges was in line with the x-axis of the coordinate system. Then a pin was pinned in the point of origin (shown by a small circle in the diagram). Another pin was placed on a random point of the circle which was on the positive side of the y-axis. Then we used our own eyesight to place the third and final pin, located next to the glass slab so that when seen through the glass, the pins appear to be perfectly aligned. However, what we see through the glass has already been refracted, so the pins will then indicate the refracted light ray. When the angle had been indicated on the graph sheet using a pencil and a ruler. This was repeated for seven different angles of incidence.
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Hanne Martine G. Ræstad
1.j Physics
25.03.2014
Raw Data
Since Snell’s law includes the sine of the angles and not the angles themselves, this is what we will try to find. Using the coordinate system and circle we drew on the graph paper, we can find two right-angled triangles for every light ray that was traced – one for the angle of incidence ( ) and one for the angle of refraction ( ). We know that the radius of the circle is 10 centimetres, which is the hypotenuse of both triangles. Using the graph paper, we can measure the lengths opposite to the angles ( ). With this information, we can find the sine of both angles, as
Which means that
and
.
This can be calculated for each angle and put into a table. Angle 1
Length x [cm] 2.0
sin(i) 0.2
Length y [cm] 1.4
2
sin(r) 0.14
Hanne Martine G. Ræstad
2 3 4 5 6 7
1.j Physics
0.5 5.0 8.0 4.0 6.0 7.0
0.05 0.5 0.8 0.4 0.6 0.7
25.03.2014
0.35 3.3 5.4 2.65 4.0 4.75
0.035 0.33 0.54 0.265 0.4 0.475
Processed data Using the same data which was used to make the table, we can make a graph of the relation between the sines of angles of incidence and refraction. Since the angle of incidence was the one which was changed in order to measure the angle of refraction, the sine of the angle of incidence will be the independent variable. The sine of angle of refraction is the dependent variable. Due to this, the sine of angle of incidence is placed on the x-axis, and the sine of angle of refraction is placed on the y-axis.
The slope of the graph will give us
. This is, however, not what we need for the formula. We can
then rewrite the formula so that we can use the information we have. Snell’s law states that
, which in this case would be
In the case of air, This is because
, where c is the velocity of light in vacuum, and v is
the velocity of light in the medium. In the case of air, the difference between these two is negligible and they are given the same value. So
= 1
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38 0
Hanne Martine G. Ræstad
1.j Physics
25.03.2014
Substituting the value for the refractive index of air, we now get this formula.
We can inverse this so that we can insert the slope value from earlier.
And so, to isolate , we can multiply both sides by and divide them by the slope of the graph.
If we then insert the value of the slope which can be read from the graph, we have found the refractive index of our glass slab.
0
Conclusion Percentage error The refractive index of glass varies depending on what type of glass the glass slab is made from, ranging from around 1.33 to 1.6. To calculate the percentage error, we will use an approximate average of 1.5 as the standard value.
00
00 00
Evaluation The percentage error is negligible. This points towards that Snell’s law is indeed correct and can be used to calculate the refractive index of any given medium if one has access to sufficient data. Snell’s law is thereby verified until otherwise proven.
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