1. Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 25

2. 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 = I m (sin  /  ) 2 =  Nearest minima  What is m for our  ?  a sin  = m  m =  Between 3 and 4, closer to 3

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

4. Diffraction and Interference

5. 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)

6. 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

7. Diffraction Envelope

8. 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

9. 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  Note that a and b are in radians

10. 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 

11. Next Time  Read: 36.9

12. If the width of the slit and the wavelength of light doubles, what happens to the space between minima? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled

13. 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 rad b)2.8X10 -7 rad c)0.005 rad d)0.6 rad e)279.5 rad