Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 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 = I m (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 = I m (cos 2  ) [(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 