phys2401 formulas
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Law of Reflection
 θ_{r} = θ_{i}
 angle of reflection = angle of incidence

Radius of Curvature
 r = 2f
 (radius) = 2 * (focal length)

Mirror/Thin Lens Equation
 1/d_{o} + 1/d_{i }= 1/f
 1 / (distance of object) + 1 / (distance of image) = 1 / (focal length)

Lateral Magnification
 m = h_{i}/h_{o} = d_{i}/d_{o}
 (magnification) = (height of image) / (height of object) = (distance of image) / (distance of object)
 note:  is sign convention

Index of Refraction
 n = c/v
 (index of refraction) = (speed of light in vacuum) / (speed of light in given material)

Snell's Law
 n_{1}sinθ_{1} = n_{2}sinθ_{2}
 (index of refraction_{1}) * (sine of angle_{1}) = (index of refraction_{2}) * (sine of angle_{2})_{}
 note: if n_{2} > n_{1}, then θ_{2} < θ_{1}.
 ie: if light goes to a medium with higher n (and speed is less), ray is bent toward the normal and vice versa.

Critical Angle
 sinθ_{c} = n_{2}/n_{1}
 (sine of critical angle) = (index of refraction_{2}) / (index of refraction_{1})

Power of Lens
 P = 1/f
 (power) = 1 / (focal point)
 note: unit is diopter, m^{1}, (1/m)

Angular Magnification/Magnifying Power
 M = θ'/θ = (h/f)/(h/N)
 (angular magnification) = θ_{with lens} / θ_{unaided }= [(height of object) / (focal length)] / [(height of object) / (near point of eye)]
 note: N for normal eye is 25

Wavelength in Another Medium
 λ_{n} = λ/n
 (wavelength in new medium) = (wavelength in air) / (index of refraction of new medium)

Interference Equations
 Constructive: dsinθ = mλ
 Destructive: dsinθ = (m+1/2)λ
 (distance between slits) * (sine of angles made with horizontal) = (order + n) * (wavelength)
 note: m = 0, 1, 2, ...

Diffraction Equation
 Dsinθ = mλ
 (slit width) * (sine of angle of rays) = (order) (wavelength)
 note: m = +/1, +/2, +/3, ...

Rayleigh Criterion
 λ = 1.22λ/D
 (resolvable angle) = 1.22 * (wavelength) / (diameter of lens)

Resolving Power (microscope)
 RP = s = fθ = 1.22λf/D
 (resolving power) = (actual distance barely resolvable) = (focal point) * (subtended angle) = 1.22 * (wavelength) * (focal length) / (diameter of lens)

Diffraction Grating equation
 dsinθ = mλ
 (distance between slits) * (sine of angles made with horizontal) = (order) * (wavelength)
 note: m = 0, 1, 2, ...

Bragg Equation
 2dsinĪ = mλ
 (distance between atoms) * (sine of measured angle) = (order) * (wavelength)
 note: m = 0, 1, 2, ...

Polarization Equation
 I = I_{0}cos^{2}θ
 (intensity of polarized light) = (incoming intensity) * (cosine of angle between polarizer and incoming light)^{2}

Brewster's Law
 tanθ_{p} = n_{2}/n_{1}
 (tangent of polarizing angle) = (index of refraction_{2}) / (index of refraction_{1})