Double Slit Diffraction

Physics 202Professor Lee

CarknerLecture 27

PAL #26 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 ? m = (a sin / = 3.33

Double Slit Diffraction

Each maxima had the same peak intensity

Double slit diffraction produces a pattern that is a combination of both 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 What you see on the screen at a given spot depends on both

interference and diffraction

Remember that a location in the pattern is defined by

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 large (d) the interference fringes are narrower and closer together

In an otherwise identical set-up a maxima for red

light will be at a larger angle than the same maxima for blue light

For solving diffraction/interference problems: 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

Diffraction Gratings

Get one maxima for each wavelength

If we increase the number of slits (N) to very large numbers (1000’s) the individual maxima (called lines) become narrow

A system with large N is called a diffraction grating Used for spectroscopy, the determination of a

materials properties through analysis of the light it emits at different wavelengths

Maxima From Grating

Diffraction Grating

Location of Lines

The angular position of each line is given by:d sin = m

The m=0 maxima is in the center, and is flanked by a broad minima and then the m=1 maxima etc.

Called an order

Orders

Resolving Power and Dispersion

Narrow lines that are well spread out

R = Nm

D = m / (d cos ) To get a large resolving power and

dispersion want a grating with many slits that are very close together

Emission Lines of Hydrogen

Using Gratings Heat up a gas that is composed of a certain

element (e.g. hydrogen) and pass the light through a grating

Rather than a continuous spectrum of all colors, the gas only produces light at certain wavelength called spectral lines

By passing the light through a grating we can see these spectral lines and identify the element