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# Physics ## Chapter 25: Wave Optics ### 25.1 Interference #### Conditions for Interference * **Coherent Sources:** Maintain a constant phase with respect to each other. * **Monochromatic:** Single wavelength. #### Constructive Interference * The path difference is zero or an integral mu...

# Physics ## Chapter 25: Wave Optics ### 25.1 Interference #### Conditions for Interference * **Coherent Sources:** Maintain a constant phase with respect to each other. * **Monochromatic:** Single wavelength. #### Constructive Interference * The path difference is zero or an integral multiple of the wavelength. * Phase difference: $2\pi, 4\pi, 6\pi,...$ #### Destructive Interference * The path difference is an odd multiple of a half wavelength. * Phase difference: $\pi, 3\pi, 5\pi,...$ #### Young's Double-Slit Experiment * **Bright Fringes (Constructive Interference):** $d \sin\theta = m\lambda$ where $m = 0, \pm1, \pm2,...$ * **Dark Fringes (Destructive Interference):** $d \sin\theta = (m + \frac{1}{2})\lambda$ where $m = 0, \pm1, \pm2,...$ * **Fringe Spacing ($\Delta y$):** $\Delta y = \frac{\lambda L}{d}$ where: * $\lambda$ = wavelength of light * $L$ = distance from slits to screen * $d$ = separation between slits #### Intensity in Double-Slit Interference * $I = I_{max} \cos^2(\frac{\pi d \sin\theta}{\lambda})$ ### 25.2 Diffraction #### Diffraction * The bending of waves as they pass through an opening or around an obstacle. #### Single-Slit Diffraction * **Dark Fringes (Destructive Interference):** $w \sin\theta = m\lambda$ where $m = \pm1, \pm2, \pm3,...$ * **Width of Central Maximum:** $2\theta = \frac{2\lambda}{w}$ #### Diffraction Grating * **Bright Fringes (Constructive Interference):** $d \sin\theta = m\lambda$ where $m = 0, 1, 2, 3,...$ * $d = \frac{1}{N}$ where $N$ is the number of lines per unit length. #### Diffraction and Resolution * **Rayleigh's Criterion:** Two images are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other. * **Resolution of a Single-Slit Aperture:** $\theta_{min} = \frac{\lambda}{w}$ * **Resolution of a Circular Aperture:** $\theta_{min} = 1.22 \frac{\lambda}{D}$ where: * $D$ = diameter of the aperture ### 25.3 Polarization #### Polarization * The process of transforming unpolarized light into polarized light. #### Methods of Polarization * **Selective Absorption** * **Reflection** * **Scattering** * **Double Refraction** #### Malus's Law * $I = I_0 \cos^2\theta$ where: * $I_0$ = initial intensity of the polarized light * $\theta$ = angle between the light's polarization direction and the transmission axis of the polarizer. #### Polarization by Reflection * **Brewster's Angle:** $\tan\theta_p = \frac{n_2}{n_1}$ where: * $\theta_p$ = polarizing angle * $n_1$ = refractive index of the initial medium * $n_2$ = refractive index of the reflecting medium