Double Slit Diffraction

1. Double Slit Diffraction Physics 202 Professor Lee Carkner Lecture 27

2. PAL #26 Diffraction • Single slit diffraction, how bright is spot 10 cm from center? • l = 680 nm, a = 0.25 mm, D = 11 m • tanq = y/D, q = arctan (y/D) = 0.52 deg • a = (pa/l)sin q = 10.5 rad • Nearest minima • a sin q = ml • Between 3 and 4, closer to 3

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

4. Diffraction and Interference

5. Double Slit Pattern • The outer diffraction envelope is defined by: a sin q =ml • The positions of the interference maxima (bright fringes) is given by: • a,d and l are properties of the set-up, q indicates a position on the screen and there are two separate m’s (one for the diffraction and one for the interference)

6. 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 q, depends on both of the m’s • To figure out which interference maxima are in the region solve for the interference m’s

7. Diffraction Envelope

8. 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

9. Intensity • The intensity in double slit diffraction is a combination of the diffraction factor: • and the interference factor: • The combined intensity is: I = Im (cos2b) (sin a / a)2

10. 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

11. Maxima From Grating

12. Diffraction Grating

13. Location of Lines • The angular position of each line is given by: d sin q = ml • For polychromatic light each maxima is composed of many narrow lines (one for each wavelength the incident light is composed of)

14. Grating Path Length

15. 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

16. Line Profile

17. 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?