Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 27

PAL #26 Diffraction  Single slit diffraction, how bright is spot 10 cm from center?  = 680 nm, a = 0.25 mm, D = 11 m   tan  = y/D,  = arctan (y/D) = 0.52 deg    = (  a/ )sin  = 10.5 rad   Nearest minima   a sin  = m   Between 3 and 4, closer to 3

Double Slit Diffraction  In double slit interference we assumed a vanishingly narrow slit and got a pattern of equal sized (and equally bright) maxima and minima   In single slit diffraction we produced a wide, bright central maximum and weaker side maxima  Double slit diffraction produces a pattern that is a combination of both 

Diffraction and Interference

Double Slit Pattern  The outer diffraction envelope is defined by: a sin  =m    The positions of the interference maxima (bright fringes) is given by:  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  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   To figure out which interference maxima are in the region solve for the interference m’s 

Diffraction Envelope

Diffraction Dependencies  For large (a) the diffraction envelopes become 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

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  For double slit interference the maxima are fairly broad   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 and is useful for spectroscopy

Maxima From Grating

Diffraction Grating

Location of Lines  The angular position of each line is given by: d sin  = m    For polychromatic light each maxima is composed of many narrow lines (one for each wavelength the incident light is composed of)

Grating Path Length

Line Width   The half-width (angular distance from the peak to zero intensity) of a line is given by:   where N is the number of slits and d is the distance between 2 slits

Line Profile

Using Gratings  If the number of rulings is very large the lines become very narrow    What can we learn by taking the light from something and passing it through a grating?     