IB Physics HL - Topic 9

displacement starting at equilibrium

x = x0sin(ωt) where ω is the angular frequency (2pi*f)

displacement starting at maximum

x = x0cos(ωt) where ω is the angular frequency (2pi*f)

Energy changes in SHM

total energy is constant, KE is max at 0 displacement, PE is max at max and min displacement

the angle of diffraction for first minimum in single slit diffraction

wavelength/widthof slit

Single Slit Diffraction condition for a minimum

width*sin(θ) = mλ

Width of bright spot in Single-Slit Diffraction (y)

y = mλD/a

Young's double slit experiment

light is projected onto a screen with 2 small slits. The light waves diffracting through the 2 slits interfere with one another and produce a predictable pattern of alternating light and dark bands (maxima and minima) on the detector screen

double slit diffraction maxima equation

distance between slits*sinθ = mλ

double-slit minima equation

distance between slits*sinθ = (m+1/2)λ

thin film interference

a phenomenon in which a spectrum of colors is produced due to the constructive and destructive interference of light waves reflected in a thin film

Thin-film interference phase shift

reflected waves have a 180 degree (1/2λ) phase shift when n2 > n1. reflected waves have no phase shift when n1 > n2

Multiple slit diffraction maxima equation

distance between slits*sinθ = mλ

thin film interference destructive interference equation

2dn = mλ

thin film interference constructive interference equation

2dn = (1/2 + m)λ where d = thickness of film, n = index of refraction in film, m = order, λ = wavelength of light

wave-particle duality

the concept that all matter and energy exhibit both wave-like and particle-like properties

Resolution

the ability to distinguish two separate points

Larger aperture

more resolved

Raleigh criterion

when two points are just resolved, θ = 1.22λ/diameter of aperture

Source moving toward observer

subtraction in denominator

Source moving away from observer

addition in denominator

observer moving toward stationary source

addition in numerator

observer moving away from stationary source

subtraction in numerator

values in moving observer situation

velocity of wave changes, wavelength is constant, frequency changes

values in moving source situation

velocity of wave is constant, wavelength changes, frequency changes

doppler equation for electromagnetic waves

change in f / original f = v/c, should only be used when v is much smaller than the speed of light