SP Unit 2.4

Practicals

Waves

SP Unit 2.4 Practicals Waves Learners should be able to demonstrate and apply their knowledge and understanding of:
1.	Measurement of intensity variation for Polarization

Measurement of Intensity Variation for Polarization
⇒ Objective
To investigate the relationship between the transmitted light intensity and the angle between the polarization direction of incident light and the axis of an analyzing polarizer, and to verify Malus’s Law:
[math]I = I_0 \cos^2 \theta[/math]
Where:
– I is the transmitted intensity,
– [math]I_o[/math] is the maximum intensity when the polarizer and analyzer are aligned,
– θ is the angle between their transmission axes.
⇒ Apparatus
Light Source:
A coherent light source such as a laser, or an unpolarized source (e.g., an incandescent lamp) combined with a polarizer to produce linearly polarized light.
Polarizer:
A device that converts unpolarized light into linearly polarized light.
Analyzer:
A second polarizing filter mounted on a rotating stage with an angular scale.
Photodetector/Light Sensor:
A photodiode or light meter to measure the intensity of the light transmitted through the analyzer.
Data Logger (Optional):
For recording intensity measurements automatically.
Protractor or Angular Scale:
To measure the angle between the polarizer and analyzer accurately.
Figure 1
⇒ Experimental Setup
1. Polarized Light Generation:
If your light source is unpolarized, first direct the light through a polarizer. This produces a beam of linearly polarized light with maximum intensity [math]I_o[/math] when the light is fully transmitted.
2. Mounting the Analyzer:
Place the analyzer (a second polarizer) in the beam path. Mount it on a rotational stage that allows you to adjust its angle θ relative to the fixed polarizer.
3. Detection System:
Position the photodetector behind the analyzer to measure the intensity of the light transmitted through both polarizers.
⇒ Procedure
1. Alignment:
Set the analyzer’s transmission axis to be parallel to that of the initial polarizer (i.e., [math]θ = 0^0[/math]).
Measure and record the maximum intensity [math]I_o[/math] using the photodetector.
2. Data Collection:
Rotate the analyzer gradually, for example in increments of 10° or 15°.
At each angle θ, record the transmitted light intensity I.
Continue the process until the analyzer has rotated through 90° (or even up to 180° to observe the full periodic behavior).
3. Graphing and Analysis:
Plot the measured intensity I versus the angle θ.
According to Malus’s Law, the relationship should follow:
[math]I = I_0 \cos^2 \theta[/math]
Alternatively, you can plot I against [math] \cos^2 \theta[/math]. This should yield a straight line with slope equal to [math]I_o[/math] if the law holds true.
Figure 2 Graphically analysis
⇒ Discussion and Error Considerations
Verification of Malus’s Law:
Compare your experimental data with the theoretical prediction. A good fit indicates that the polarizers are working properly and that the light is indeed linearly polarized.
Sources of Error:
– Ambient Light: Ensure that extraneous light does not affect the photodetector readings.
– Imperfections in Polarizers: Real polarizers may not be 100% efficient, which can cause deviations.
– Measurement Accuracy: Accurate angle measurement is crucial. Ensure the rotational stage is well-calibrated.
Data Reproducibility:
Repeating the experiment multiple times and averaging the results can help reduce random errors and improve reliability.
⇒ Conclusion
This experiment demonstrates the concept of polarization and confirms Malus’s Law, showing that the intensity of transmitted light through an analyzer varies as the cosine squared of the angle between the polarizer and analyzer. It is a fundamental demonstration of the wave nature of light and the properties of polarized light, with applications ranging from optical filters to liquid crystal displays.