10Class 12 Physics

Wave Optics formulas

Young's double slit, diffraction and polarisation formulas for Wave Optics. Path difference is the idea behind almost all of it.

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Interference

Bright fringes: $\displaystyle \Delta x = n\lambda$
Constructive, n = 0, 1, 2, ...
Dark fringes: $\displaystyle \Delta x = \left(n + \tfrac12\right)\lambda$
Destructive.
Path difference in YDSE: $\displaystyle \Delta x = \frac{yd}{D}$
Fringe width: $\displaystyle \beta = \frac{\lambda D}{d}$
Resultant intensity: $\displaystyle I = I_1 + I_2 + 2\sqrt{I_1I_2}\cos\phi$
Phase from path: $\displaystyle \phi = \frac{2\pi}{\lambda}\Delta x$

Minima of a single slit: $\displaystyle a\sin\theta = n\lambda$
n = 1, 2, 3, ...
Width of the central maximum: $\displaystyle w = \frac{2\lambda D}{a}$

Confusing the two conditions. In YDSE, nλ gives bright fringes, while in single-slit diffraction a sin θ = nλ gives dark ones.
Forgetting a fringe pattern changes in water. The wavelength becomes λ/n, so the fringes get narrower.
Applying Malus's law to unpolarised light. A polaroid passes half the intensity of unpolarised light.

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