Double Slit Diffraction

Physics 202Professor Lee

CarknerLecture 25

PAL #24 Diffraction Single slit diffraction, how bright is spot 5 cm from

center? = 680 nm, a = 0.25 mm, D = 5.5 m tan = y/D, = arctan (y/D) = 0.52 deg = (a/)sin = 10.5 rad I = Im(sin/)2 =

Nearest minima What is m for our ? a sin = m m = Between 3 and 4, closer to 3

Double Slit Diffraction

Each maxima had the same peak intensity In single slit diffraction we produced a wide,

bright central maximum and weaker side maxima

The interference maxima are modulated in intensity by a broad diffraction envelope

Diffraction and Interference

Double Slit Pattern The outer diffraction envelope is defined by:

a sin =m

Between two minima, instead of a broad diffraction maxima will be a pattern of interference fringes

d sin = m a,d and are properties of the set-up, indicates a

position on the screen and there are two separate m’s (one for the diffraction and one for the interference)

Patterns

e.g. You would expect the m = 5 interference maxima would be bright, but if it happens to fall on the m = 3 diffraction minima it will be dark

What you see at a certain angle , depends on both of the m’s We can use the location of two adjacent diffraction minima (sequential

diffraction m’s) to define a region in which may be several interference maxima

i.e. first define the diffraction envelope, then find what interference orders are inside

Diffraction Envelope

Diffraction Dependencies

For longer wavelengths, the fringes are further apart

For solving diffraction/interference problems: Can find the diffraction minima with a sin =m Can find the interference maxima with d sin

=m There are two different m’s

Intensity The intensity in double slit

diffraction is a combination of the diffraction factor:

and the interference factor:

The combined intensity is:

I = Im (cos2 ) [(sin / ]2

Note that a and b are in radians

Angle and Distance Note that for any interference or

diffraction pattern you can translate between angles () and distance on the screen (y)

tan = y/D

y

D

Next Time

Read: 36.9

If the width of the slit and the wavelength of light doubles, what happens to the space between minima?

a) Quarteredb) Halvedc) Stays the samed) Doublede) Quadrupled

If the Hubble Space Telescope has an aperture of 2.4 meters and observes at 550 nm, what is the smallest angle it can resolve?

a) 3.4X10-9 radb) 2.8X10-7 radc) 0.005 radd) 0.6 rade) 279.5 rad