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CLASS 12 • PHYSICS
Wave Optics
1. Wavefronts
Phase Difference ($\phi$)
$\phi = \frac{2\pi}{\lambda} \Delta x$
$\Delta x$ = Path Difference
Intensity (Superposition)
$I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$
Max Intensity ($I_{max}$)
$I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2$
If $I_1=I_2=I_0$, then $I_{max} = 4I_0$
2. Interference vs Diffraction
| Feature | Interference (YDSE) | Diffraction (Single) |
|---|---|---|
| Bright Fringe | $\Delta x = n\lambda$ | $\Delta x = (n + \frac{1}{2})\lambda$ |
| Dark Fringe | $\Delta x = (n + \frac{1}{2})\lambda$ | $\Delta x = n\lambda$ |
| Width | All Equal Width | Central Max is Double |
| Intensity | All Equal Brightness | Decreases rapidly |
3. YDSE Experiment
Fringe Width ($\beta$)
$\beta = \frac{\lambda D}{d}$
D = Slit-Screen dist, d = Slit gap
Position of nth Bright
$y_n = \frac{n \lambda D}{d} = n\beta$
Angular Width
$\theta = \frac{\lambda}{d}$
Independent of D
4. Single Slit Diffraction
Linear Width (Central)
$W = \frac{2\lambda D}{a}$
$a$ = Width of slit
Angular Width (Central)
$2\theta = \frac{2\lambda}{a}$
Resolving Power (Microscope)
$RP = \frac{2\mu \sin\theta}{1.22 \lambda}$
Fresnel Distance
$Z_F = \frac{a^2}{\lambda}$
5. Polarization
Malus Law
$I = I_0 \cos^2\theta$
Between Polarizer & Analyzer
Brewster's Law
$\mu = \tan i_p$
Reflected & Refracted rays are $\perp$
Unpolarized Light
$I_{transmitted} = \frac{I_0}{2}$
After passing 1st polaroid
6. Common Exam Traps
- ⚠️ The "n" Trap: In Diffraction, Minima is at $n\lambda$. In Interference, Maxima is at $n\lambda$. They are REVERSED!
- ⚠️ Water Immersion: If YDSE setup is dipped in water ($\mu$), wavelength decreases ($\lambda' = \lambda/\mu$). So Fringe Width $\beta$ DECREASES.
- ⚠️ Missing Fringes: If slit width $a$ is large, diffraction envelope limits the number of interference fringes seen.
7. Golden Theory Rules
- Coherent Sources: Must have constant phase difference. Two independent bulbs can NEVER be coherent.
- Wavefronts: Point source $\to$ Spherical. Line source $\to$ Cylindrical. Distant source $\to$ Plane.
- Conservation: Interference redistributes energy (Dark $\to$ Bright). It does NOT create or destroy energy. Average intensity remains same.
