Introduction to Light and Optics Equations

Introduction to
Light and Optics

EQUATIONS

INFORMATION

Energy of a Photon

$Energy of a Photon$

$\\ \bold{E} = energy \hspace{4} of \hspace{4} a \hspace{4} photon \hspace{4} (J) \\ \bold{h} = Planck's \hspace{4} constant \hspace{4} (6.625 \hspace{2}x \hspace{2} 10^{-34} J \hspace{2} s ) \\ \bold{\nu} = frequency \hspace{4} of \hspace{4} the \hspace{4} light \hspace{4}(Hz) \\ \bold{c} = speed \hspace{4} of \hspace{4} light \hspace{4} (3.0 \hspace{2} x \hspace{2} 10^8 \hspace{4} m \hspace{2} s^{-1}) \\ \bold{\lambda} = wavelength \hspace{4} (m)$

Index of Refraction

$Index of Refraction$

$\\ \bold{v} = velocity \hspace{4} of \hspace{4} light \hspace{4} in \\ \indent \hspace{4} medium \hspace{4} (m \hspace{2} s^{-1}) \\ \bold{c} = speed \hspace{4} of \hspace{4} light \\ \indent \hspace{4} (3.00 \hspace{2} x \hspace{2} 10^8 \hspace{2} m \hspace{2} s \hspace{2}^{-1}) \\ \bold{n} = index \hspace{4} of \hspace{4} refraction$

Reflection

$Reflection$

$\\ \bold{\theta_i} = angle \hspace{4} of \hspace{4} incidence \hspace{4} (deg) \\ \bold{\theta_r} = angle \hspace{4} of \hspace{4} reflection \hspace{4} (deg)$

Total Internal Reflection

$Total Internal Reflection$

$\\ \bold{\theta_c} = critical \hspace{4} angle \hspace{4} (deg) \\ \bold{n_\&hash;} = index \hspace{4} of \hspace{4} refraction \hspace{4} of \\ \indent \hspace{12} medium \hspace{4} \&hash;$

Wave Under Refraction

$Wave Under Refraction$

$\\ \bold{\theta_1} = angle \hspace{4} of \hspace{4} incidence \hspace{4} (deg) \\ \bold{\theta_2} = angle \hspace{4} of \hspace{4} refraction \hspace{4} (deg) \\ \bold{v_\&hash;} = speed \hspace{4} of \hspace{4} light \hspace{4} in \\ \indent \hspace{12} medium \hspace{4} \&hash;$

Snell's Law

$Snell's Law$

$\\ \bold{n_{\&hash;}} = absolute \hspace{4} index \hspace{4} of \hspace{4} refraction \\ \indent \hspace{10} of \hspace{4} \&hash; \hspace{4} medium \\ \bold{\theta{\&hash;}} = angle \hspace{4} (deg)$

Lateral Magnification

$Lateral Magnification$

$\\ \bold{M} = lateral \hspace{4} magnification \\ \bold{h'} = image \hspace{4} height \hspace{4} (m) \\ \bold{h} = object \hspace{4} height \hspace{4} (m) \\ \bold{q} = image \hspace{4} distance \hspace{4} (m) \\ \bold{p} = object \hspace{4} distance \hspace{4} (m)$

Angular Magnification

$Angular Magnification$

$\\ \bold{m} = angular \hspace{4} magnification \\ \bold{\theta} = angle \hspace{4} subtended \hspace{4} by \hspace{4} \\ \indent \hspace{4} object \hspace{4} with \hspace{4} a \hspace{4} lens \hspace{4} in \hspace{4} use \hspace{4} \\ \bold{\theta_0} = angle \hspace{4} subtended \hspace{4} by \hspace{4} \\ \indent \hspace{9} object \hspace{4} with \hspace{4} no \hspace{4} lens \hspace{4} in \hspace{4} use \hspace{4} \\$

F-Number

$F-Number$

$\\ \bold{N} = f-number \\ \bold{f} = focal \hspace{4} length \hspace{4} (m) \\ \bold{D} = diameter \hspace{4} of \hspace{4} entrance \hspace{4} pupil \hspace{4} (m)$

Focal Length (Spherical Mirror)

$Focal Length (Spherical Mirror)$

$\\ \bold{f} = focal \hspace{4} length \hspace{4} (m) \\ \bold{R} = radius \hspace{4} of \hspace{4} the \hspace{4} mirror \hspace{4} (m)$

Mirror Equation (Spherical Mirror)

$Mirror Equation (Spherical Mirror)$

$\\ \bold{p} = object \hspace{4} distance \hspace{4} (m) \\ \bold{q} = image \hspace{4} distance \hspace{4} (m) \\ \bold{f} = focal \hspace{4} length \hspace{4} (m)$

Image Formation by Refraction (Spherical Interface)

$Image Formation by Refraction (Spherical Interface)$

$\\ \bold{n_\&hash;} = index \hspace{4} of \hspace{4} refraction \hspace{4} of \\ \indent \hspace{13} media \hspace{4} \&hash; \\ \bold{p} = object \hspace{4} distance \hspace{4} (m) \\ \bold{q} = image \hspace{4} distance \hspace{4} (m) \\ \bold{R} = radius \hspace{4} (m)$

Lens - Makers' Equation

$Lens - Makers' Equation$

$\\ \bold{f} = focal \hspace{4} length \hspace{4} of \hspace{4} a \hspace{4} thin \\ \indent \hspace{4} lens \hspace{4} surrounded \hspace{4} by \hspace{4} air \hspace{4}(m) \\ \bold{n} = index \hspace{4} of \hspace{4} refraction \hspace{4} of \hspace{4} lens \\ \bold{R_1} = radius \hspace{4} of \hspace{4} curvature \\ \indent \hspace{14} closest \hspace{4} to \hspace{4} light \hspace{4} (m) \\ \bold{R_2} = radius \hspace{4} of \hspace{4} curvature \\ \indent \hspace{13} furthest \hspace{4} from \hspace{4} light \hspace{4} (m)$

Thin Lens Equation

$Thin Lens Equation$

$\\ \bold{p} = distance \hspace{4} from \hspace{4} object \hspace{4} to \hspace{4} lens \hspace{4} (m) \\ \bold{q} = distance \hspace{4} from \hspace{4} image \hspace{4} to \hspace{4} lens \hspace{4} (m) \\ \bold{f} = focal \hspace{4} length \hspace{4}(m)$

Maximum Magnification

$Maximum Magnification$

$\\ \bold{m_{max}} = maximum \hspace{4} magnification \\ \bold{f} = focal \hspace{4} length \hspace{4}(cm)$

Overall Magnification by Compound Microscope

$Overall Magnification by Compound Microscope$

$\\ \bold{M} = overall \hspace{4} magnification \\ \bold{L} = distance \hspace{4} between \hspace{4} lenses \hspace{4} (cm) \\ \bold{f_0} = focal \hspace{4} length \hspace{4} of \hspace{4} objective \hspace{4} (cm) \\ \bold{f_e} = focal \hspace{4} length \hspace{4} of \hspace{4} eyepiece \hspace{4} (cm)$

Angular Magnification of a Refracting Telescope

$Angular Magnification of a Refracting Telescope$

$\\ \bold{m} = angular \hspace{4} magnification \\ \bold{f_0} = focal \hspace{4} length \hspace{4} of \hspace{4} objective \hspace{4} (m) \\ \bold{f_e} = focal \hspace{4} length \hspace{4} of \hspace{4} eyepiece \hspace{4} (m)$

Intensity

$Intensity (Double - Slit Interference)$

$\\ \bold{I} = intensity \hspace{4} (W \hspace{2} m^{-2}) \\ \bold{I_{max}} = maximum \hspace{4} intensity \hspace{4} (W \hspace{2} m^{-2}) \\ \bold{d} = distance \hspace{4} between \hspace{4} slits \hspace{4} (m)\\ \bold{\theta} = angle \hspace{4} between \hspace{4} fringes \hspace{4} (deg)\\ \bold{\lambda} = wavelength \hspace{4} (m)$

Double-Slit Interference (Dark Spots)

$Double-Slit Interference (Dark Spots)$

$\\ \bold{d} = distance \hspace{4} between \hspace{4} slits \hspace{4} (cm) \\ \bold{\theta} = angle \hspace{4} between \hspace{4} fringes \hspace{4} (deg) \\ \bold{n} = order \hspace{4} of \hspace{4} the \hspace{4} fringe \\ \bold{\lambda} = wavelength \hspace{4} of \hspace{4} light \hspace{4} (cm)$

Double-Slit Interference (Bright Spots)

$Double-Slit Interference (Bright Spots)$

Rayleigh Criterion (Single Slit)

$Rayleigh Criterion (Single Slit)$

$\\ \bold{\alpha_c} = Rayleigh \hspace{4} criterion \hspace{4} (rad) \\ \bold{\lambda} = average \hspace{4} wavelength \hspace{4} of \hspace{4} light \\ \indent \hspace{4} contributing \hspace{4} to \hspace{4} image \hspace{4} (m) \\ \bold{a} = width \hspace{4} of \hspace{4} slit \hspace{4} (m)$

Rayleigh Criterion (Circular Aperture)

$Rayleigh Criterion (Circular Aperture)$

$\\ \bold{\alpha_c} = Limit \hspace{4} of \hspace{4} Angular \hspace{4} Resolution / \\ \indent \hspace{10} Rayleigh \hspace{4} criterion \hspace{4} (rad) \\ \bold{\lambda} = average \hspace{4} wavelength \hspace{4} of \hspace{4} light \\ \indent \hspace{4} contributing \hspace{4} to \hspace{4} image \hspace{4} (m) \\ \bold{D_o} = aperture \hspace{4} (m)$

Brewster's Law

$Brewster's Law$

$\\ \bold{\theta} = Brewster's \hspace{4} angle \hspace{4} (deg) \\ \bold{n_2} = index \hspace{4} of \hspace{4} refraction \hspace{4} of \hspace{4} the \\ \indent \hspace{12} initial \hspace{4} medium \\ \bold{n_1} = index \hspace{4} of \hspace{4} refraction \hspace{4} of \hspace{4} the \\ \indent \hspace{12} reflecting \hspace{4} medium$

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