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Law of Reflection
- θr = θi
- angle of reflection = angle of incidence
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Radius of Curvature
- r = 2f
- (radius) = 2 * (focal length)
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Mirror/Thin Lens Equation
- 1/do + 1/di = 1/f
- 1 / (distance of object) + 1 / (distance of image) = 1 / (focal length)
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Lateral Magnification
- m = hi/ho = -di/do
- (magnification) = (height of image) / (height of object) = -(distance of image) / (distance of object)
- note: - is sign convention
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Index of Refraction
- n = c/v
- (index of refraction) = (speed of light in vacuum) / (speed of light in given material)
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Snell's Law
- n1sinθ1 = n2sinθ2(index of refraction1) * (sine of angle1) = (index of refraction2) * (sine of angle2)
- note: if n2 > n1, then θ2 < θ1.
- ie: if light goes to a medium with higher n (and speed is less), ray is bent toward the normal and vice versa.
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Critical Angle
- sinθc = n2/n1(sine of critical angle) = (index of refraction2) / (index of refraction1)
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Power of Lens
- P = 1/f
- (power) = 1 / (focal point)
- note: unit is diopter, m-1, (1/m)
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Angular Magnification/Magnifying Power
- M = θ'/θ = (h/f)/(h/N)
- (angular magnification) = θwith lens / θunaided = [(height of object) / (focal length)] / [(height of object) / (near point of eye)]
- note: N for normal eye is 25
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Wavelength in Another Medium
- λn = λ/n
- (wavelength in new medium) = (wavelength in air) / (index of refraction of new medium)
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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, ...
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Diffraction Equation
- Dsinθ = mλ
- (slit width) * (sine of angle of rays) = (order) (wavelength)
- note: m = +/-1, +/-2, +/-3, ...
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Rayleigh Criterion
- λ = 1.22λ/D
- (resolvable angle) = 1.22 * (wavelength) / (diameter of lens)
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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)
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Diffraction Grating equation
- dsinθ = mλ
- (distance between slits) * (sine of angles made with horizontal) = (order) * (wavelength)
- note: m = 0, 1, 2, ...
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Bragg Equation
- 2dsinĪ = mλ
- (distance between atoms) * (sine of measured angle) = (order) * (wavelength)
- note: m = 0, 1, 2, ...
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Polarization Equation
- I = I0cos2θ
- (intensity of polarized light) = (incoming intensity) * (cosine of angle between polarizer and incoming light)2
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Brewster's Law
- tanθp = n2/n1(tangent of polarizing angle) = (index of refraction2) / (index of refraction1)
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