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Thin Lens Equation

1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

OpticsPhysicsRelates a thin lens's focal length to its object and image distances.

Lens Magnification (m = −d_i/d_o)

m=−didom = -\frac{d_i}{d_o}

OpticsPhysicsImage magnification from the ratio of image to object distance; the minus sign tracks inversion.

Magnification from Heights (m = h_i/h_o)

m=hihom = \frac{h_i}{h_o}

OpticsPhysicsMagnification as the ratio of image height to object height.

Focal Length of a Spherical Mirror

f=R2f = \frac{R}{2}

OpticsPhysicsA spherical mirror focuses parallel rays at half its radius of curvature.

Snell's Law of Refraction

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2

OpticsPhysicsLight bends at an interface so that n sin θ stays the same on both sides.

Index of Refraction (n = c/v)

n=cvn = \frac{c}{v}

OpticsPhysicsHow much a medium slows light: the ratio of c to the speed of light in the medium.

Critical Angle for Total Internal Reflection

sin⁡θc=n2n1\sin\theta_c = \frac{n_2}{n_1}

OpticsPhysicsBeyond this angle of incidence, light in the denser medium reflects totally instead of refracting.

Brewster's Angle

tan⁡θB=n2n1\tan\theta_B = \frac{n_2}{n_1}

OpticsPhysicsThe incidence angle at which reflected light is completely polarized.

Lens Power in Diopters

P=1fP = \frac{1}{f}

OpticsPhysicsThe optician's unit: lens power in diopters is the reciprocal of focal length in meters.

Double-Slit Fringe Spacing

Δy=λLd\Delta y = \frac{\lambda L}{d}

OpticsWaves & OscillationsPhysicsSpacing between adjacent bright fringes on a screen a distance L behind two slits d apart.

Diffraction Grating Equation

mλ=dsin⁡θm \lambda = d \sin\theta

OpticsWaves & OscillationsPhysicsBright beams leave a grating at angles where the path difference d sin θ is a whole number of wavelengths.

Apparent Depth

d′=dnd' = \frac{d}{n}

OpticsPhysicsViewed from straight above, an object under water appears at depth d/n.

Thin-Film Constructive Interference (Bright Reflection)

2nt=(m+12)λ2 n t = \left(m + \tfrac{1}{2}\right)\lambda

OpticsWaves & OscillationsPhysicsBright-reflection condition for a thin film with one half-wave inversion: twice the optical thickness is a half-odd number of wavelengths.

Thin-Film Destructive Interference (Dark Reflection)

2nt=mλ2 n t = m \lambda

OpticsWaves & OscillationsPhysicsDark-reflection condition for a thin film with one half-wave inversion: twice the optical thickness is a whole number of wavelengths.