Lecture Notes: Wave Optics and Polarization
Introduction
- Lecturer/Instructor: Rajwan Singh
- Topic: Wave Optics, Polarization and Diffraction
Wave Optics (Class 12)
- Overview: Comparative easier for students who have studied Class 12 well.
- Topics Covered:
- Interference: Constructive and Destructive
- YDSE (Young's Double Slit Experiment)
- Diffraction
- Polarization
Interference
- Constructive Interference:
- Occurs when Crest overlaps with Crest and Trough with Trough.
- Resultant Amplitude increases.
- Equation:
y = A sin(ωt + φ) where φ = Δx * (2π / λ)
- Destructive Interference:
- Occurs when Crest overlaps with Trough.
- Amplitude decreases.
- Conditions:
- Constructive Interference:
Δx = nλ
- Destructive Interference:
Δx = (2n-1) * λ / 2
YDSE (Young's Double Slit Experiment)
- Setup: Two slits
S1 and S2 with distance d apart.
- Key Formulas:
- Path Difference:
Δx = d sin θ
- Fringe Width (β):
β = λD / d
- Position of Fringes:
- Bright Fringes:
x = nλD / d
- Dark Fringes:
x = (2n-1) * λD / (2d)
- **With Different Conditions: **
- If slits have different widths, intensities vary.
- Intensity Formula:
I = I1 + I2 + 2√(I1 I2) * cos(φ)
- Fraunhofer Diffraction Conditions: Small angles, large screen distance.
Polarization
- Definition: Restriction of light oscillation to one plane.
- **Types: **
- Unpolarized Light: Electric fields oscillate in multiple planes.
- Polarized Light: Electric fields oscillate in one plane.
- Polarizers and Analyzers:
- Polarizer: Material that polarizes light (e.g., calcite).
- Analyzer: Used to examine polarized light.
- Law of Malus:
- Intensity of polarized light:
I = I0 * cos² θ*
Diffraction
- Definition: Bending of light around obstacles comparable to wavelength.
- Single Slit Diffraction:
- Central Maximum highest intensity.
- Conditions for Minima:
a sin θ = nλ
- Intensity Distribution:
I = I0 * (sin β / β)² where β = (πa/λ) sin θ
- Diffraction Grating: Multiple slits, sharper maxima.*
Important Points
- Polarization by Reflection (Brewster's Angle):
- Angle at which reflected light is completely polarized.
- Brewster's Law:
tan θ_B = n.
- Fringe Visibility: Contrast between maxima and minima.
Example Problems:
- YDSE with different slit widths: Calculate maxima and minima intensities.
- Polarization: Calculate transmitted intensity after multiple polarizers.
- Diffraction: Identify angles for minima in single slit experiment.
Remember to revise and practice questions related to these concepts for a thorough understanding.