Optics and waves flashcards

It includes all common optics/wave equations, due note theres basically no contextual discription so youll need to look that up

Snells law

sin(θ₁)n₁= sin(θ₂)n₂

Critcal Angle

when n₁>n₂ total internal reflection occurs at angles above θ_c = arcsin(n₂/n₁)

lens/mirror equation based off object distance

1/f = 1/d_o + 1/d_i

o = object distance, i=image distance

Magnification equation

m = -d_o/d_i

m = -h_o/h_i

-m = inverted image

Lensmaker’s equation

1/f = (n-1)(1/R₁ - 1/R₂)

R = radius of curvature(one for each side)

n = index of refraction

-useful when they give you two seperate radius for a two sided lense

Mirror equation

f = R/2

Optical Power

P = 1/f

D = diopters, unit for lense strength

Double-Slit Interference(Bright fringes)

dsin(θ) = mλ

where m = 0, ±1, ±2, and determines what interference fringe is being specifically being referred too

Double-slit small-angle formula

y_m=mλL/d

y_m= verticle position of mth bright fringe on the background

λ = wavelength of light through slits

L = Distance from slits to screen

d = seperation between two slits

Dark fringes

dsin(θ) = (m+1.5)λ

-same as the bright fringe but half a phase off

Braggs law

λm = 2dsin(θ)

d = distance between lattices

-used in xray crystallography  

Brewster's Angle

tan(θ) = n₂/n₁

-the angle at which light is completely polarized when entering a new medium

Malus’s law

I = I_icos²(θ)

-calculates the intensity of light through polarizers

-for when its in series recalculate the angle change between polarizers and repeat

Rayleigh Criterion

θ_min = 1.22λ/D

D = aperture diameter

-Resolution limit because of diffraction

-shorter wavelength and large aperture means higher resolution

Wave speed

v = fλ

-most basic wave equation

-f is frequency, lamda is wavelength

Wave speed on rope or string

v = √(T/μ)

T = tension of string or rope

μ = linear mass density

Wave speed in solid rod or bulk medium

v = √(E/ρ)

E = Young’s Modulas(materials resistance to deformation along one axis) ρ = density

v = √(B/ρ)

B = Bulk Modulas(resistance to deformation from all directions)

standing wave on string(fixed on both ends)

λ = 2L/n, n is an integer, n=1 equals the first harmonic, n=2 equals the first overtone

f_n = nv/2L, same rules apply

nodes = n+1 antinodes = n

Standing wave in air column(both ends open)

λ = 2L/n,

f_n = nv/2L, same rules apply

-same as standing wave fixed at both

nodes = n+1 antinodes = n

Standing wave in air column(one end closed)

λ = 4L/n,

f_n = nv/4L

-n must be an odd integer

nodes = n antinodes = (n+1)

Doppler effect

f' = f[(v + v_o)/(v + v_s)]

v = wave speed v_s = source speed v_o= observer speed

Decibel Intensity

β = 10 log₁₀(I/I₀)

I₀ = 10⁻¹² W/m²

+10 dB = 10× intensity increase; +3 dB ≈ 2× intensity

Lorenz Factor