Multiple-Slit Interference Uniform slits, distance d apart. Light of wavelength. Screen L away “Thin” slits  compared to d) L >> d then path length difference between ADJACENT SLITS

For MAXIMUM amplitude of combined waves (“totally constructive interference”), need: Multiple-Slit Interference Maxima

Multiple-Slit Interference Minima More difficult: need to consider # of slits/sources 2 slits 3 slits Try: get

N = 2 d = 0.1 mm = 700 nm N = 3 d = 0.1 mm = 700 nm N = 4 d = 0.1 mm = 700 nm N = 5 d = 0.1 mm = 700 nm

N = 2 d = 0.1 mm = 700 nm N = 3 d = 0.1 mm = 700 nm N = 4 d = 0.1 mm = 700 nm N = 5 d = 0.1 mm = 700 nm

ConcepTest #42: The interference pattern of four (thin) slits equally spaced a distance d apart is shown. Consider the following choices:  2.  /45. 3  /2 3.  /26. 2  (back of card) None of the above a) What is the phase difference between adjacent slits for the CENTRAL MAXIMUM? b) What is the phase difference between adjacent slits for the FIRST SIDE MINIMUM? c) What is the phase difference between adjacent slits for the 2 nd SIDE MINIMUM? d) What is the phase difference between adjacent slits for the 3 rd SIDE MINIMUM?

L y Example: Multiple Slit Interference Pattern Light of wavelength is incident on four (thin) slits equally spaced a distance d apart. The interference pattern is shown on a screen a distance L away. What is the distance y, from the center of the screen to the first side minimum? What is the angular width of the central maximum? What happens as you decrease d ?

 First side minimum condition (for FOUR narrow slits)

N = 5 d = 0.1 mm = 700 nm N = 5 d = 0.09 mm = 700 nm N = 5 d = 0.08 mm = 700 nm N = 5 d = 0.07 mm = 700 nm

Diffraction Grating (better to think of it as an Interference Grating) Multiple Slit Interference LOTS of Slits VERY thin VERY CLOSELY spaced Examples: Diffraction Grating from lab Laser Vision Glasses CD (reflection grating) ConcepTest #43: You look at a bright source of white light through a diffraction grating. Looking away from the center, you will see colors. What color will you see closest to the center? 1. Red4. Green 2. Orange5. Blue 3. Yellow6. Violet (back of card) Not enough info Think about This: What will you see at the center?

N = 5 d = 0.1 mm = 700 nm N = 5 d = 0.1 mm = 600 nm N = 5 d = 0.1 mm = 500 nm N = 5 d = 0.1 mm = 400 nm

Single Slit Diffraction top bottom

Single Slit Diffraction MINIMA occur at Multiple Slit Interference (principal) MAXIMA occur at

Single Slit DiffractionTwo Slit Interference (thin slits) a d

Resolution & Diffraction

y x Rectangular aperture Circular aperture “Rayleigh’s Criterion”

Circular aperture, far field (Fraunhofer) Circular aperture, near field, (Fresnel) Circular obstruction Poisson/Fresnel bright spot