Student’s Name
: IMRAN BIN ARIFFIN
Partner’s Name
: Muhammad Fakhruddin Bin Ghazali
Class
: E11C
Teacher’s Name
: Pn. Adilah bt. Che Hassan
Date
: 31.01.2012
TITLE
: Verifying Snell’s Law
Aim
: To verify Snell’s Law by finding the refractive index .
Problem Defining: Defining: Snell’s law, which states that the refractive refractive index
ratio where
,
of a medium is equal to the
is respectively angle of incident incident and angle of refraction, can be verified from
a constant gradient of the graph against where is the reciprocal of the gradient. But since the angle of refraction has its limit i.e. when total internal reflection occurs, the graph is constant only for critical angle . Therefore we may only consider the gradient for .
Research Question: To verify Snell’s Law by showing that the ratio of the sin value of incident angle to the sine of refracted angle is a constant and is equal to the refractive index of the glass, by measuring the respective angle made by the bent light ray to the normal at the point of bending when a light ray is projected trough a glass block at different angle. Variables:
Independent Variable: the incident angles Dependent Variable: the refractive angle
of the light ray to the normal of glass block.
of the light ray to the normal of glass block.
Constant Variable: the refractive index of the glass i.e. same glass block, position of glass block, the colour of light ray (constant degree of refraction), length r of radial lines. Materials and Apparatuses: a rectangular glass block, a small protractor, a big protractor, a wide white paper, light ray projector, sharp mechanical pencil.
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Methods for Controlling Variables: The lights are turned off and curtains are closed to maximize the relative intensity of the light ray (to make easy to observe and to mark the angles). The glass block used is the same throughout the experiment for constant refractive index n. T he experiment is made on wide white paper to maximize clarity for observation. A very sharp mechanical pencil is used to mark the angles, in order to produce accurate measurement. Lines r are made to help in determining the position from which light ray is to be projected for respective . More values of are anticipated to be used near the critical angle since the markings might get narrower causing it hard to measure the angle . As to maintain the position of glass block, lines parametering the glass block are drawn before the experiment to allow the x and z position of the glass block is constant hence a constant normal line can be used.
Methods for Collecting Variables and the Precaution Measures:
The values of is produced by first drawing markings using protractor and then radial lines from the center O through the respective markings are made to help with light ray projection. During the projection of the light ray, we make sure that the ray is always at the center of and parallel to the respective radial line so that the angle made by ray to the normal is the same as that by the radial line. After the light is on, we make radial lines for each of the markings so that we can measure from respective radial lines using a protractor. As precaution measures in collecting the data,
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Diagram:
Procedure: A wide white paper is let to spread flat on a wide table. A dot O as the point of refraction is drawn on the centre of the paper and then a long straight line named the boundary line is drawn through it such that it is almost perpendicular to one side of the paper. From referenced at the line, ticks showing angles , whose measurement start from the line, from 0 to 90 of interval 10 (except for angle 82 ) are made using a big protractor and a sharp mechanical pencil Then, straight lines radiating from O through the ticks are drawn. Another long straight line is drawn perpendicular to the first one and is considered the normal line.
A glass block is put on the paper such that point O touches one of its sides and that side fully touches the boundary line(as in the diagram).
Following the methods for controlling variables and for collecting data stated up above, th e procedure continues. At angle of incident, , of 10.00 light ray is projected and the produced angle of refraction, , is measured and the value is recorded. The experiment is repeated with of .
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Data Collection and Processing
10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 82.0
6.00 13.5 19.0 26.0 30.5 36.5 39.0 41.0 41.5
0.174 0.342 0.500 0.643 0.766 0.866 0.940 0.985 0.990
0.009 0.008 0.008 0.007 0.006 0.004 0.003 0.002 0.001
Sample Calculations: 1. For
2. Uncertainty for : By using
We get
( ) ( ) ( )
And hence
√ ( ) ( ) (eq. 1)
0.105 0.233 0.326 0.438 0.508 0.595 0.629 0.656 0.663
0.009 0.008 0.008 0.008 0.008 0.007 0.007 0.007 0.007
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For
and
:
√ ( ) ( )
From (eq. 1) and
:
0.800
0.700 Y=0.670
0.600
0.500 ) r _ a t e h t ( n i s
0.400
0.300
0.200
0.100
0.000
y = 0.6796x - 0.0072
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*the centroid, C of the graph:
( )
From the graph and from the equation
The gradient, m, of the graph:
We get
is the gradient m of the graph, hence
Uncertainty of n, as from the graph,
Where max gradient,
And minimum gradient,
Mean gradient
Hence
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Conclusion and Evaluation The refractive index , n, of the glass is the ratio of the sine value of incident angle to the sine value of angle of refraction and holds a constant constant value which is equal to 1.50 1
The theoretical refractive index is 1.50 so percentage error,
Since all %Error <
| | | | | | ,
The result is acceptable since the results are within the range of possible values of i.e. within the uncertainty. From the small value of y-intercept from this graph, it shows that the systematic error in this experiment is little.
The green dotted vertical straight line from the graph showing shows that the domain of the x-axis is limited to 1.00. Another similar, horizontal line shows the range of y-axis values is limited to 0.670. this means that critical angle of glass, as from this experiment, is 42.1 , which is near enough to the theoretical value of
But still further revisions on the methods for controlling variables to further increase t he accuracy and precision thus the reliability of this experiment. So, the experiment is needed to be repeated with suggestions mentioned in the table below. For reducing percentage error, below are some considered limitations and suggested methods for improvement. Evaluation:
The lines are drawn at both sides of the glass block produce unnecessary uncertainties and inaccuracy in measurement of since markings needed to be made on the boundary of glass block, which is hard to do. So, Instead of using rectangular glass block for refraction, we found out that it is easier to produce accurate result using semi-circular glass block. Because unl ike rectangular glass block, semi-circular one will make sure that any light ray passing through its curved boundary and its center point O is refracted only once, which is at the linear boundary, since the at the first boundary, the ray is at 90
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So, Since the dispersion increases by length travelled, we need to minimize the length travelled prior to second bend. So, we need to project the light ray as close as possible to the glass block.
As the gets higher, the closer if the gap between each marking. As it gets very close it is hard to make the marking and measure the angle using protractor. The lines r we made radiating from the refraction point O to the respective markings are too short for a highly sensitive and accurate measurement of using the small protractor.
We should increase the length L so a new glass block with a length much greater than L is needed to replace it. As L increases, the length of the radiating lines r will increase hence the possible value of maximum and minimum will increase as a result, meaning the ‘trueness’ of measured increases (as in the diagram):
