Lecture Notes: Double Slits and Diffraction Gratings

Introduction to Double Slits

• Purpose: Demonstrate light's wave-like interference patterns.
• Experiment:
  • Shine a green laser through double slits.
  • Observe bright and dark spots blending on a screen.
• Challenges:
  • Measuring angles and distances is difficult due to smudginess of spots.
  • Bright spots fade quickly, often hard to see beyond the 5th or 6th spot.

Enhancing the Experiment

• Solution: Create more holes, spaced at distance D.
• Effect:
  • Results in defined dots instead of smudgy patterns.
  • Dots are brighter and extend further.

Explanation of Pattern Formation

• Wave Travel:
  • Each wave travels a certain distance to reach the wall.
  • Constructive interference occurs when waves are integer multiples of wavelengths apart.
• Example with Two Holes:
  • 1st wave travels a base distance.
  • 2nd wave travels one wavelength further for constructive interference.
• Example with Additional Holes:
  • 3rd wave travels two wavelengths further than the 1st.
  • Each subsequent wave continues this pattern.

Constructive and Destructive Interference

• Constructive Interference:
  • Peaks match peaks, valleys match valleys.
  • Occurs at specific integer wavelengths, resulting in bright spots.
• Destructive Interference:
  • Occurs when deviations from integer wavelengths cause waves to cancel each other out.
  • Pairing of waves results in zero intensity away from bright spots.

Advantages of Multiple Holes

• Diffraction Grating:
  • Multiple holes create clearer and separate bright spots.
  • Bright spots are more intense and last longer.
• Measurement:
  • Easier to measure distances between dots due to lack of smudginess.
  • Brighter and more defined dots.

Diffraction Grating

• Definition: An array of thousands of closely spaced holes.
• Lines per Centimeter:
  • Typically have thousands of lines per centimeter.
  • Lines are the blocked parts; holes are the unblocked parts.
• Mathematical Relationship:
  • Formula: (d \sin \theta = m \lambda)
  • Remains valid for diffraction gratings, determines constructive interference points.