Interference Physics 202 Professor Lee Carkner Lecture 24

Interference   Due to a phase difference between the incoming waves the amplitude of the resultant wave can be larger or smaller than the original   Light can experience such interference as well   The interference of light demonstrates the wave nature of light

The Wave Nature of Light   Example: why does refraction occur?   A wavefront produces spherical wavelets which propagate outward to define a new wavefront

Huygen’s Principle

Refraction and Waves  In a vacuum each subsequent wavefront is parallel to the last   As a wavefront enters a medium with a larger index of refraction part of the wavefront is in the new medium and part is out   Some wavelets lag behind others so the new wavefront is bent  If you consider a ray perpendicular to the wavefronts, it is also bent

Huygen and Snell

Snell’s Law  n = c/v  v is the velocity in the medium  sin  1 / sin  2 = v 1 / v 2  sin  1 /sin  2 = n 2 /n 1  Which is Snell’s Law: n 1 sin  1 = n 2 sin  2

Velocity and Wavelength    Its velocity is equal to c only in vacuum   Light also changes wavelength in a new medium   If the new n is larger, v is smaller and so is smaller   Frequency stays the same

Phase Change   If light travels through a medium of length L with index of refraction n, the number of wavelengths in that medium is:  Consider two light rays that travel the same distance, L, through two different mediums  N 2 - N 1 = (L/ )(n 2 -n 1 )

Phase  We can represent phase in different ways   Phase differences are seen as brightness variations  Constructive interference  Destructive interference  Intermediate interferences produces intermediate brightness

Different n’s

Diffraction   When a planar wavefront passes through a slit the wavefront flares out   Diffraction can be produced by any sharp edge  e.g. a circular aperture or a thin edge

Diffraction

Diffraction of a Telescopic Image of the Pleiades

Basic Interference  Interference was first demonstrated by Thomas Young in 1801   The slits produce two curved wavefronts traveling towards a screen   The interference patterns appear on the screen and show bright and dark maxima and minima, or fringes

Interference

Interference Patterns   The two rays travel different distances and so will be in or out of phase depending on if the difference is a multiple of 1 or an odd multiple of 0.5 wavelengths   L =  What is the path length difference (  L) for a given set-up?

Path Length Difference  Consider a double slit system where d is the distance between the slits and  is the angle between the normal and the point on the screen we are interested in    L = d sin   This is strictly true only when the distance to the screen D is much larger than d

Path Length

Maxima and Minima  d sin  = m  For minima (dark spots) the path length must be equal to a odd multiple of half wavelengths: d sin  = (m+½)

Location of Fringes  You can locate the position of specific fringes if you know the value of m (called the order)  For example: m=1    Zeroth order maxima is straight in front of the slits and order numbers increase to each side

Interference Patterns  You can also find the location of maxima in terms of the linear distance from the center of the interference pattern (y):  For small angles (or large D) tan  = sin  y = m D/d   The same equation holds for for minima if you replace m with (m+½)

Wavelength of Light   Young first did this in 1801, finding the average wavelength of visible sunlight   The measurement is hard to make because is small

Coherence  Light sources that have a constant phase difference are called coherent   Any two random rays from a laser will be in phase   The phase difference varies randomly   We have assumed coherence in our derivation