Lab Manual - Malus's Law Verification

Verification of Malus's Law

Laboratry Manual

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1 Aim

To verify Malus’s law which states that the intensity of polarized light transmitted through an analyzer varies as the square of the cosine of the angle between the transmission axes of the polarizer and analyzer.

2 Apparatus Used

  • Light source (LED or Laser)
  • Polarizer (Fixed)
  • Analyzer (Rotatable)
  • Photodetector or Light sensor
  • Digital multimeter
  • Rotating mount with angular scale
  • Optical bench
  • Connecting wires

3 Diagram

Malus’s Law

4 Theory

When unpolarized light passes through a polarizer, it becomes linearly polarized. If this polarized light then passes through a second polarizer (called an analyzer), the intensity of the transmitted light depends on the angle θ between the transmission axes of the polarizer and analyzer.

According to Malus's Law, discovered by Étienne-Louis Malus in 1808, the intensity of light transmitted through the analyzer is given by:

$I = I_0 \cos^2\theta$

Where:

  • I = Intensity of transmitted light
  • I₀ = Intensity of incident polarized light
  • θ = Angle between polarizer and analyzer axes

This law demonstrates that:

  • Maximum transmission occurs when θ = 0° (parallel axes)
  • Minimum transmission (zero) occurs when θ = 90° (crossed axes)
  • The relationship follows a cosine-squared dependence

5 Formula

Malus's Law:
$I = I_0 \cos^2\theta$
Normalized Form:
$\frac{I}{I_0} = \cos^2\theta$
For Verification:
$\sqrt{\frac{I}{I_0}} = |\cos\theta|$

6 Procedure

1 Set up the optical bench with light source, polarizer, analyzer, and photodetector in sequence.
2 Connect the photodetector to the digital multimeter to measure the output voltage (proportional to light intensity).
3 Switch on the light source and allow it to stabilize for a few minutes.
4 Align the polarizer and analyzer axes parallel (θ = 0°) and record the maximum intensity I₀.
5 Rotate the analyzer in steps of 10° from 0° to 180° and record the corresponding intensity values.
6 For better accuracy, take readings while rotating the analyzer in both clockwise and counterclockwise directions.
7 Record all observations in the observation table.

7 Observation Table

Sr. No. Angle θ (degrees) cos θ cos² θ Observed Intensity I (mV) I/I₀ % Error
11.0001.000
210°0.9850.970
320°0.9400.883
430°0.8660.750
540°0.7660.587
650°0.6430.413
760°0.5000.250
870°0.3420.117
980°0.1740.030
1090°0.0000.000

Note: I₀ = Maximum intensity at θ = 0° = _____ mV

8 Calculations

Percentage Error Calculation:
$\text{Error \%} = \frac{|\text{Theoretical} - \text{Observed}|}{\text{Theoretical}} \times 100\%$
$\text{Error \%} = \frac{|\cos^2\theta - \frac{I}{I_0}|}{\cos^2\theta} \times 100\%$

Sample Calculation:

For θ = 30°:

  • Theoretical value: cos²(30°) = (0.866)² = 0.750
  • If observed I = 375 mV and I₀ = 500 mV
  • Then I/I₀ = 375/500 = 0.750
  • Error % = |0.750 - 0.750|/0.750 × 100% = 0%

9 Result

The experimental results verify Malus's Law within acceptable experimental error limits. The intensity of transmitted polarized light follows the relationship:

$I = I_0 \cos^2\theta$

Key Observations:

  • Maximum transmission occurs at θ = 0° (parallel polarizers)
  • Minimum transmission occurs at θ = 90° (crossed polarizers)
  • The intensity variation follows the predicted cosine-squared relationship
  • Average percentage error: _____%

Conclusion: Malus's Law is successfully verified experimentally.

10 Precautions

  • Ensure proper alignment of all optical components on the bench.
  • Allow the light source to stabilize before taking readings.
  • Handle polarizers carefully to avoid scratches or fingerprints.
  • Take multiple readings and calculate average values for better accuracy.
  • Ensure the photodetector is properly calibrated and connected.
  • Avoid stray light by conducting the experiment in a darkened room.
  • Rotate the analyzer slowly and steadily for consistent readings.
  • Check for zero error in the measuring instruments before starting.
  • Maintain constant distance between components throughout the experiment.
  • Record the angular positions carefully using the graduated scale.

11 Viva Voice Questions

1 Q: What is Malus's Law and who discovered it?
A: Malus's Law states that the intensity of polarized light transmitted through an analyzer varies as the square of the cosine of the angle between the transmission axes. It was discovered by Étienne-Louis Malus in 1808.
2 Q: What happens when θ = 0° and θ = 90°?
A: At θ = 0°, maximum light is transmitted (I = I₀). At θ = 90°, no light is transmitted (I = 0) as the polarizers are crossed.
3 Q: What is the difference between polarizer and analyzer?
A: A polarizer converts unpolarized light into polarized light. An analyzer is used to analyze the polarization state of already polarized light.
4 Q: What are the applications of polarization?
A: Sunglasses, LCD displays, photography filters, stress analysis, optical instruments, and 3D cinema technology.
5 Q: How does a photodetector work in this experiment?
A: The photodetector converts light intensity into electrical signals (voltage/current) which can be measured and is proportional to the incident light intensity.
6 Q: What is the mathematical form of Malus's Law?
A: I = I₀ cos²θ, where I is transmitted intensity, I₀ is incident intensity, and θ is the angle between polarizer axes.
7 Q: What causes the experimental errors in this experiment?
A: Misalignment of components, stray light, instrumental errors, non-ideal polarizers, and environmental factors.

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