Wave Optics — Complete Formula

Superposition Principle

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Resultant Displacement	[y = y_1 + y_2]	[y_1, y_2] = individual wave displacements	m	Basic principle ⭐

💡 Memory Hint:
Waves overlap → add displacements

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Path Difference	[\Delta x = n\lambda]	[\Delta x] = path difference, [\lambda] = wavelength	m	Constructive interference ⭐
Destructive Condition	[\Delta x = (2n+1)\dfrac{\lambda}{2}]	[n] = integer	m	Destructive interference ⭐
Fringe Width	[\beta = \dfrac{\lambda D}{d}]	[\beta] = fringe width, [D] = screen distance, [d] = slit separation	m	Very important ⭐
Position of Fringes	[y_n = n\beta]	[y_n] = position	m	Regular spacing

💡 Memory Hint:
Fringe width ∝ wavelength & distance

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Fringe Width	[\beta = \dfrac{\lambda D}{d}]	—	m	Core formula ⭐
Intensity	[I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi]	[\phi] = phase difference	W/m²	Interference pattern ⭐

💡 Memory Hint:
Equal intensities → clear fringes

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Condition (Minima)	[a\sin\theta = n\lambda]	[a] = slit width	—	Dark fringes ⭐
Angular Width	[\theta = \dfrac{\lambda}{a}]	—	rad	Central maximum ⭐
Linear Width	[W = \dfrac{2\lambda D}{a}]	[W] = width	m	Very important ⭐

💡 Memory Hint:
Narrow slit → wider diffraction

Concept	Formula	Symbols Meaning	SI Units	Key Notes
Resolving Power	[RP = \dfrac{1}{d} = \dfrac{2\mu \sin\theta}{\lambda}]	[\mu] = refractive index	—	Smaller λ → better resolution ⭐

Concept	Formula	Symbols Meaning	SI Units	Key Notes
Resolving Power	[RP = \dfrac{D}{1.22\lambda}]	[D] = aperture	—	Larger aperture → better ⭐

💡 Memory Hint:
Better resolution → smaller wavelength

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Malus Law	[I = I_0 \cos^2\theta]	[I_0] = initial intensity	W/m²	Polarization effect ⭐
Brewster’s Law	[\tan\theta_B = n]	[\theta_B] = Brewster angle	—	No reflection ⭐

💡 Memory Hint:
Polarization proves light is transverse

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Condition	Same frequency & constant phase	—	—	Needed for interference ⭐

💡 Memory Hint:
Stable phase → stable pattern

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Intensity ∝ Amplitude²	[I \propto A^2]	[A] = amplitude	—	Basic relation ⭐
Max Intensity	[I_{max} = ( \sqrt{I_1} + \sqrt{I_2} )^2]	—	W/m²	Constructive ⭐
Min Intensity	[I_{min} = ( \sqrt{I_1} – \sqrt{I_2} )^2]	—	W/m²	Destructive ⭐

💡 Memory Hint:
Brightness depends on amplitude squared

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