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Optics: Exploring Diffraction, Interference, and Polarization in A-Level Science
Fundamentals of Light Behavior
Optics examines wave phenomena including diffraction (bending around obstacles), interference (wave superposition), and polarization (directional oscillation).
Core Principles
Diffraction
Single-Slit Diffraction:
\[
a\sin\theta = n\lambda \quad \text{(for minima)}
\]
Where:
- \(a\): Slit width (m)
- \(\theta\): Angular position (°)
- \(n\): Order number (1,2,3…)
- \(\lambda\): Wavelength (m)
Interference
Double-Slit Interference:
\[
\Delta y = \frac{\lambda D}{d}
\]
Where:
- \(\Delta y\): Fringe spacing (m)
- \(D\): Screen distance (m)
- \(d\): Slit separation (m)
Polarization
Malus’ Law for polarized light intensity:
\[
I = I_0\cos^2\theta
\]
Modern Applications
Imaging Technology
- Diffraction-limited resolution: \( \theta \approx 1.22\lambda/D \)
- Polarizing filters reduce glare by 90%
Fiber Optics
- Total internal reflection: \( \theta_c = \sin^{-1}(n_2/n_1) \)
- Single-mode fibers maintain interference patterns
Scientific Instruments
- Polarimeters measure sugar concentrations
- Interferometers detect nanometer displacements
Worked Example
Double-Slit Experiment:
- \(\lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m}\)
- \(D = 2 \, \text{m}\)
- \(d = 0.01 \, \text{m}\)
\[
\Delta y = \frac{(500 \times 10^{-9})(2)}{0.01} = 0.1 \, \text{mm}
\]
Common Pitfalls
- Using slit width (\(a\)) instead of separation (\(d\)) in interference
- Forgetting \(n\) starts at 1 for diffraction minima
- Neglecting intensity reduction in polarized light
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