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Formula Sheets / Physics

Chapter 27

Wave Optics

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Interference (YDSE)Diffraction Polarisation

Interference (YDSE)

Fringe width
$β = \frac{λ D}{d}$
Path difference
$Δ x = \frac{y d}{D};$ bright: $Δ x = nλ;$ dark: $Δ x = (2 n - 1) \frac{λ}{2}$
Intensity
$I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ;$ $\frac{I _{m a x}}{I _{m i n}} = (\frac{I _{1} + I _{2}}{I _{1} - I _{2}})^{2}$
Thin slab in one path
shift $= \frac{( n - 1 ) t D}{d}$
In a medium
$β^{'} = \frac{β}{n}$

Diffraction

Single slit minima
$a sin θ = nλ;$ central maximum width $= \frac{2 λ D}{a}$
Resolving power
$θ_{m i n} = \frac{1.22 λ}{D}$ (telescope)
Fresnel distance
$z_{F} = \frac{a ^{2}}{λ}$

Polarisation

Malus's law
$I = I_{0} cos^{2} θ;$ unpolarised through a polaroid: $\frac{I _{0}}{2}$
Brewster's law
$tan θ_{B} = n;$ $θ_{B} + r = 9 0^{\circ}$

Ray Optics Dual Nature of Matter