Semi-cilinder Optical Behavior
Description of the Experiment
This experiment has multiple purposes:
- Determine the refraction index of Plexiglas and verify Snell's law;
- Measure the critical angle at which there is total internal reflection;
- Study the power transmited and reflected in an optical interface, proving conservation of energy;
- Study the power transmited and reflected as a function of laser polarization, determining Brewster's angle.
This analisis can be done qualitatively by processing the picture from the camera or quantitatively by using the light sensor that sweeps the semicilinder angle-wise. Because of experimental constraints, the avaliable angle range is only 0º through 240º.
- Video: rtsp://elabmc.ist.utl.pt/optica.sdp
- Laboratory: Intermediate at e-lab.ist.eu
- Control room: optica
- Level: ****
The ray tracer mode allows a qualitative analysis of the transmission and reflection of light in the interface between Plexiglas and air through the pictures captured by the camera.
The user chooses the starting and ending angle for the sweep. With some pictures and Snell's law it is possible to calculate the refraction index for the denser material (Plexiglas). We suggest using an image processing software like Corelpaint, Photoshop or Draw (openoffice.org) to analyse the pictures: simply find the light rays and measure the angle between them.
Note: selecting angles between 0º and 180º means the light will shine upon the curved side of the semi-cylinder, whereas between 180º and 360º the light will shine on the straight side.
In "direct light" mode, the user selects the angle at which light shines upon the cylinder, and during the experiment itself the output will be the laser's intensity. Usually, two maxima can be found when sweeping the circle: one is the transmitted ray and the other the reflected one. At 0º, the user can determine the laser's absolute power. We also suggest angles in [90º:180º] to study the Plexiglas-air interface and [270º-360º] for air-Plexiglas interface. This procedure can be done with; (i) non-polarized light, (ii) vertically polarized light, (iii) horizontally polarized light.
According to Snell's Law, there is an angle (it's called the Critical Angle, and only exists in the case of light crossing from a optically denser material to a lesser one) where there is no transmitted beam, because the incident beam was completely reflected in the contact surface between the two materials.
After determining the refraction index (Protocol I), this angle can be calculated, and the user can verify through experiment that there is no transmission beyond it. We recommend looking at the reflected and transmitted power in the neighborhood of this angle, through small increases and find a mathematical function that best fits these points. The angles used should be between 90º and 180º (these correspond to a transition from the denser material to the less dense one).
After polarizing the laser beam, we notice that the light behaves differently in the transitions (Protocolo II). Specifically, there is an angle (called Brewster's Angle) where a vertically polarized wave cannot be reflected, therefore creating a transmitted beam that is perpendicular to the incident one. The angle can be calculated using the refractive indexes.