Diffraction - ch. 36

ucla | PHYSICS 1C | 2023-03-18T20:06

Definitions

diffraction is the effect of the edge of shadows forming bands and not immediately light to dark
the central band may be broader than the slit and shrinks further from the center
Types of diffraction: Fresnel (near-field: point due to close source/screen), Fraunhofer (far-field: parallel rays)
Fraunhofer: dark fringes can be calculated as sources from top and center of the slit of slit width $a$

$r_{2} - r_{1} = \frac{a}{2} \sin θ ⟹ \sin θ \approx θ = \frac{m λ}{a} m \in \Z \neq 0$

$y_{m} = R \frac{m λ}{a} R » y_{m}$

$I = I_{0} [\frac{\sin (π a (\sin θ) / λ)}{π a (\sin θ) / λ}]^{2} = I_{0} [\frac{\sin (β / 2)}{β / 2}]^{2} β = \frac{2 π}{λ} a \sin θ$

$I_{m} \approx \frac{I_{0}}{(m + 1 / 2)^{2} π^{2}}$

$I = I_{0} \cos^{2} \frac{ϕ}{2} [\frac{\sin (β / 2)}{β / 2}]^{2}$

$d \sin θ = m λ m \in \Z$

diffraction from circular slit/aperture causes concentric rings of maxima
the central spot is the Airy disc - describe radius using the angular radius of first dark ring $θ_{1}$ and the wavelength and aperture diameter $D$

$\sin θ_{1} = 1.22 \frac{λ}{D} D = \frac{f}{f-number} f : focal len$

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