Refraction: The bending of the direction of travel of light as it enters a medium of different optical density.
Hypothesis:
Due to the theory that light bends when it passes from a less dense medium to a denser medium, the light ray from the light box will bend as it goes from the air into the perspex. Hence refraction of light will be seen.
Equations/Units to be used:
- Sin i
- Sin r
- Sin i/ sin r (Snell’s law)
- Critical angle (sin Ic = sin i/ sin r)
Variables:
Dependent Variable: Angle of incidence
Independent Variable: Angle of refraction
Controlled Variables:
- Material of perspex
- Intensity of light
- Frequency of light (i.e. Colour)
- Positioning of light on perspex
- Temperature of environment
- Type of perspex
- Surface on which experiment is conducted
Materials/Apparatus:
- Semi-circular perspex
- Light box
- Protractor
- Power supply
Reasons for choosing apparatus:
- Semi-circular perspex: only one point of refraction, and is more denser than air, so that refraction will be able to be seen
- Colour of light: Normal light from the light box, so that the angle of refraction could be seen better
- Light box: To obtain a beam of narrow light
- Protractor: To mark the incident angles
- Power box: To supply power to the light box
Safety Issues
- Avoid looking directly into the light source as this is harmful for the eyes.
- Be careful of electricity
Method:
- Mark and label points with a light pencil, of the various angles to be measured. (Use a protractor)
- Place the semicircular perspex block within the contours of the semicircle drawn on the grid provided.
- Shine a single ray from the ray box along the 10 degrees line and mark the position of the refracted ray with a dot and the corresponding alphabetical letter.
- Do likewise for the rest of the lines with the assigned degree value.
- Remove the perspex block and draw lines to mark each refracted ray.
- Measure the angles of refraction with the protractor and record them onto the Results Table provided.
- Do so for the rest of the Results Table.
How variables were kept constant:
The variables were kept constant by ensuring that they were controlled. The most important variable that was to be controlled was the positioning of light source, so that the light passed through the centre of the perspex.
Difficulties encountered and how they were overcome:
- Accuracy of angles: used a protractor to measure
- Accuracy of refractive angles as the beam thickened as it passed through the perspex: measured and marked a point on the grid as closely as possible to the narrowest part of the light ray.
- Ensuring that the light went through the centre of the perspex: repeated each angle 2-3 times to be sure of the results acquired
- Keeping the perspex stable: one person held the perspex while another marked the points.
Results:
The results obtained were as accurate as possible, and covered a range of angles, from 0 degrees to 80 degrees and not above that, as the light ray would have been reflected. Also, the results obtained were narrowed to + or – each side of the result. Lastly, the results from three other students in the class were compared and then averaged to ensure accuracy.
*All results to 3 significant numbers Average: 1.506
Analysis of results:
The data collected relates to the aim, as the angle of incidence and the angle of refraction, are obtained and were able to be used, to find the relationship between both sets of results.
Graphs:
Equations:
Snell’s Law
Snell's law gives the relationship between angles of incidence and refraction for a wave impinging on an interface between two media with different indices of refraction. The law follows from the boundary condition that a wave is continuous across a boundary, which requires that the phase of the wave be constant on any given plane, resulting in
where and are the angles from the normal of the incident and refracted waves, respectively.
Evaluations:
The values obtained for sin i/ sin r can all be rounded of to 1.50, which is a constant, according to Snell’s Law. This value is called the absolute refractive index, which is constant for a certain object.
From the results table, it can be seen that the values for the absolute refractive index of the perspex is approximately 1.50, which is also the theoretical value for perspex.
These values were obtained by recording the points at which the light ray bent, from air into the perspex. Hence, the constant for the perspex was able to be calculated through Snell’s Law, which states that the sine of the incident angle divided by the sine of the refractive angle will always give a constant, which is the absolute refractive index of the material being experimented with. These values also help to prove the aim, of finding a relationship between the incident and refractive angles. Also, from the graph of the sin i over sin r forms a straight line which allows us to find the gradient, using the formula on the previous page. This helps to prove that the gradient of the line is the same as the constant give by Snell’s law. However, when the graph of the incident angle over the refractive angle is plotted, it results in a curve. Hence, the gradient cannot be calculated. This proves that Snell’s law is correct.
Lastly, using Snell’s law, it can be determined that when the angle of incident is zero degrees, the angle of refraction will also be zero degrees. However, as the incident angle increases beyond the critical angle and the refracted angle increases beyond 90 degrees, the refracted ray is reflected back into the perspex, into the same plane as the incident angle. This phenomenon is called total internal reflection. This too can be calculated using Snell’s law by setting the refraction angle equal to 90°.
Inferences:
Limitations of apparatus and measuring equipment:
- Thick beam coming out from perspex, making it difficult to mark an accurate point for the refractive angle.
- The protractor, only measuring to an accuracy of 1 degree, which may cause the results to be slightly inaccurate.
- Thick refractive light ray which may have cause a difference of almost 3 degrees.
- The ray of light passing right through the middle of the perspex.
Uncertainty of data and calculations:
- Making precise, exact line of the light rays
- Parallax error
- Estimation of where to draw point
Expected and derived relationships or physical values:
- The expected result for the relationship between the incident angle and the refracted angle is a constant, 1.50 which is the relative index for the perspex. The derived results are quite accurate, due to the result being obtained and averaged out by comparing the results of three other people. However, the result can be further improved by using a grid that has the protractor printed on it. This would make it easier, to read the angle of both the incident and refracted rays.
Conclusion:
The investigation of the relationship between the incident angle and the refracted angle was a success. The absolute refractive index of perspex was proven to be 1.50, although there were slight differences in the results. Also, the investigation proved that Snell’s law is correct and that when light passes through a medium that is denser, it bends (refraction). Also, the gradient, of any graph plotted for sin i over sin r for particular material, results in a constant, which is its relative index.
Word Count: 1733 words
Bibliography:
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Date accessed: 17/04/2004
Done By:
Jitendra Jain
Year 11 A
