Edexcel A Level (IAL) Physics-2.20 Core Practical 6: Investigating Diffraction Gratings- Study Notes- New Syllabus

CORE PRACTICAL 6: Determine the Wavelength of Light Using a Diffraction Grating

This experiment uses a diffraction grating to accurately measure the wavelength of a laser or monochromatic light source. It makes use of the diffraction grating equation:

\( n\lambda = d\sin\theta \)

Apparatus

• Laser or monochromatic light source
• Diffraction grating (e.g., 300, 600, or 1000 lines/mm)
• Screen or white wall
• Metre ruler or measuring tape
• Protractor
• Retort stand and clamps

Method

1. Fix the diffraction grating securely so that the laser passes perpendicularly through it.
2. Place a screen several metres away to allow clear diffraction spots (fringes) to form.
3. Mark the central (zero-order) bright spot.
4. Mark the first-order and second-order spots on both sides.
5. Measure the horizontal distance \( x \) from the central maximum to each side maximum.
6. Measure the distance \( L \) from the grating to the screen.
7. Calculate the diffraction angle using:
   

   \( \theta = \tan^{-1}\left(\dfrac{x}{L}\right) \)

8. Find the grating spacing \( d \) using:
   

   \( d = \dfrac{1}{N} \)

   where \( N \) = lines per metre.

9. Substitute \( n \), \( d \), and \( \theta \) into:
   

   \( n\lambda = d\sin\theta \)

 Important Notes

• Ensure laser hits the grating perpendicular to its surface.
• Use measurements for left and right orders and average them.
• Higher orders increase accuracy but may be dimmer.
• Use a dark room for clearer fringes.
• Always follow laser safety precautions (never look directly into the beam).

Sample Data Table (Typical Format)

• Distance to screen: \( L = 2.50\ \mathrm{m} \)
• Measured for first order:
  • \( x_{\text{left}} = 0.82\ \mathrm{m} \)
  • \( x_{\text{right}} = 0.80\ \mathrm{m} \)
  • Average \( x = 0.81\ \mathrm{m} \)
• Diffraction grating: 600 lines/mm → \( N = 600\times10^3 = 6.00\times10^5\ \mathrm{m^{-1}} \) → \( d = \dfrac{1}{6.00\times10^5} = 1.67\times10^{-6}\ \mathrm{m} \)

 Example Calculation

Using the diffraction formula:

• Order: \( n = 1 \)
• \( d = 1.67\times10^{-6}\ \mathrm{m} \)
• \( \theta = \tan^{-1}\left(\dfrac{0.81}{2.50}\right) = 17.8^\circ \)

\( \lambda = \dfrac{d\sin\theta}{n} = \dfrac{1.67\times10^{-6} \sin 17.8^\circ}{1} = \dfrac{1.67\times10^{-6} \times 0.306}{1} = 5.11\times10^{-7}\ \mathrm{m} \)

The wavelength of the laser ≈ \( 510\ \mathrm{nm} \).

 Evaluation and Sources of Error

• Ensure grating is perpendicular to laser beam.
• Screen must be flat and directly in line with beam.
• Avoid parallax error when marking fringe positions.
• Use a longer distance \( L \) to reduce percentage uncertainty.
• Avoid stray light and reflections.

Results & Conclusion

• Using a diffraction grating gives very accurate wavelength measurements.
• More lines/mm → sharper fringes → better accuracy.
• Higher order maxima improve precision if visible.