Chapter 16

Interference and Diffraction

16.1 - InterferenceObjectives:

•Describe how light waves interfere with each other to produce bright and dark fringes

•Identify the conditions required for interference to occur

•Predict the location of interference fringes using the equation for double-slit interference

Interference

• Occurs when waves combine by superposition

• Can be constructive (resultant wave has an amplitude greater than that of any of the individual component waves)

• Can be destructive (resultant wave has an amplitude less than that of either of the individual component waves)

Constructive Interference

Destructive Interference

Interference, cont.In phase: If the crest of one wave overlaps the crest of another wave, with a phase difference of 0o

Out of phase: If the crest of one wave overlaps the trough of another wave, with a phase difference of 180o

Coherence: when the phase difference between two waves isconstant; the waves do not shift relative to each other over time

Interference

• Waves must have a constant phase difference (coherence) in order for interference to be observed.

• If interference is to be clearly observed, the interfering waves must also have the same wavelength (i.e., they must be the same color, also known as monochromatic)

• Coherence can be obtained using a single wave source. It cannot be obtained using two different sources.

Interference, cont.

Double slit wave pattern,monochromatic light

Double slit wave pattern,white light

Thin Film Interference

• Occurs due to differences in thickness of the film at various points

Thin Film Interference

Thin Film Interference notes:

Thin Film Interference

Thin Film Interference

Thin Film Interference Problems:

• Determine the type of interference that occurs in the problem: where, what kind

• Remember that the wave reflected from the lower surface of the film has to travel 2x the thickness before returning to the upper surface, where it interferes with the portion of the wave that reflects at the upper surface

Demonstrating Interference

Light passing through two narrow slits act as two light sources that are coherent.When the coherent waves constructively interfere, you see a bright stripe.When the the coherent waves destructively interfere, you see a dark stripe.The alternating dark and bright parallel bands are called fringes.

Demonstrating Interference, cont.

Predicting location of interference fringes

d

The bottom beam has to travel slightly farther than the top beam to meet at point P.This distance is called the path difference and is equal to d(sinθ), where d is the distance between the two slits. This path difference has to equal a whole number multiple of the wavelength to create constructive interference. The path difference would be a (multiple plus ½) of wavelength for destructive interference to occur.

Predicting location of interference fringes

Constructive fringes (bright) : d(sinθ) = m

m is the order number of the fringe. The center bright fringe is the zeroth order, or m=0 (when θ=0). This is also called the central maximum.The next bright fringe is the first order, m=1, etc.

Fringe calculation exampleThe distance between two slits is 0.030mm. The second-order bright fringe is measured on a viewing screen at an angle of 2.15o from the central maximum.What is the wavelength of the light?

What do we know?

d = 0.030mm = 3x10-5m

θ = 2.15o

Second order means m=2

Bright fringe means constructive interference

d(sinθ) = m

= 5.63 x 10-7m

16.2 - Diffraction

• Objectives:

• Describe how light waves diffract around obstacles and produce bright and dark fringes

• Calculate the position of fringes for a diffraction grating

• Describe how diffraction determines an optical instrument’s ability to resolve imagesnterference

Diffraction

• Is the spreading of light into a region behind an obstruction

• Occurs when waves pass through small openings, around obstacles, or by sharp edges

Interference - Coherence

• Coherence produces an interference pattern.

• In order to produce the interference pattern, the component waves producing coherence must be of the same wavelength.

Interference - Coherence

• Interference patterns are VERY predictable. These patterns are called diffraction patterns if the light comes from a single slit (various portions of a single wave interfere), but interference patterns if the waves added come from two or more openings.

Interference (Diffraction) caused by Thin Slits

• Patterns of light and dark parallel bands (fringes) appear on viewing screen

• The light fringes are due to constructive interference (light fringes are called maxima)

• The dark fringes are due to destructive interference (dark fringes are called minima)

Interference/Diffraction is caused by Three Common Types of Slits

• Single Slit

• Double Slit

• Diffraction Grating

Single slit diffraction pattern

Produces one very large, bright central maximum bandthat is twice as wide as the secondary maximas. The darkbands are called minima.

Compare to double-slit pattern….

Interference – Double Slit (Young’s)

Young’s Double Slit

Young’s Double Slit Equations

also, y/L = λ/dθ < 5o

Bright fringesd(sin θ) = mλ

Dark fringesd(sin θ) = (m + ½ )λ

Diffraction Gratings

• Use diffraction and interference to disperse light.

• If white light is used, the light will break into its component colors (like a prism)

Diffraction Gratings

• The result is separation and repeated color blocks, from m=0 (zero order) to infinity.

• In reality, only a few m values are seen.

Diffraction Gratings

Diffraction Equations for diffraction gratings

d(sin θ) = mλ m = 0, + 1, + 2, . . .

for bright fringes

y/L = λ/d will NOT work because θ > 5o

So, use tan θ = y/L to find θ

Then use d(sin θ) = mλ

Diffraction grating example problem

Monochromatic light from a helium-neon laser (=632.8nm)Shines at a right angle to the surface of a diffraction gratingthat contains 150,500 lines/m. Find the angles at which onewould observe the first and second order maxima.

Compact Discs are Diffraction Gratings

The disc has alternating rows of pits (inscribed data) and smooth surfaces. Thedata pits don’t reflect nearly as much light as the smooth surfaces in between them,And the reflected light constructively interferes. Depending on the direction of theincoming light, the orientation of the disc and the light’s wavelength, you’ll seea “rainbow” of colors coming off the disc.

Diffraction in the World

Diffraction in the World