Electric Potential

1
Interference of Light

• Intensity of double-slit pattern
• Three slits

2
Youngs Double Slit Experiment
Screen at infinity
?
d
?x
Path difference
?x d sin ?
d sin? m ?, m 0, 1, 2,
Maximum intensity at
d sin? (m ½ ) ?, m 0, 1, 2,
Minimum intensity at
3
Find the intensity of the double-slit
interference pattern as a function of position
on the screen.
Two waves E1 E0 sin(w t) E2
E0 sin(w t f )
where
4
Trigonometry sin a
sin b 2 cos (a-b)/2 sin (ab)/2
E1 E2 E0 sin(w t) sin(w t f ) 2
E0 cos (f / 2) sin(w t f / 2)
Resultant amplitude ER
Resultant intensity,
(a function of angle q to the screen)
5
I
position

• fringes are wide, with fuzzy edges
• equally spaced (in sin ? or small ?)
• equal intensity

6
Quiz
With only one slit open, the intensity in the
centre of the screen is 100 W/m 2. With both
(identical) slits open together, the intensity at
locations of constructive interference will be

1. zero
2. 100 W/m2
3. 200 W/m2
4. 400 W/m2

7
Example

• Two narrow parallel slits are separated by 0.85mm
  and are illuminated by light of a 600nm
  wavelength.
• What is the phase difference between the two
  interfering waves on a screen 2.8m away at a
  point 2.5mm from the central bright fringe?
• What is the ratio of the intensity at this point
  to the intensity at the center of a bright
  fringe?

8
(No Transcript)
9
Three Equally-Spaced Slits
?
is the phase difference between consecutive
slits
d
?x dsin?
d
Total,
10
Three Slits Pattern
The total displacement is where ?
2? (d sin? )/?

• When d sin? m ? and , ER
  3E0 (maximum value) so the bright fringes are
  in the same locations as with two slits.
• There are minima (zero intensity) at ? 120
  and ? 240 (where d sin? ?/3, 2?/3 ) to see
  this, add the first and third term above).
• At ? 180 (where d sin? ?/2) there is a small
  maximum ER E0

11
I
9I0
3 slits
I0
1/2
2/3
1
1/3
f
In wavelengths
2p/3 rad ?x ? /3
12
Differences between 2-slit and 3-slit patterns

• 3 Slits
• Main peaks become narrower brighter
• One extra faint secondary peak in between
• Main peaks (? m2p) are in the same places

As the number of slits becomes large, the main
interference fringes become even narrower and
brighter the additional numerous faint peaks
become less and less noticeable in comparison.
13
Many Slits (diffraction grating)
I
0
1
-1
m(d sin? )/?
14
Quiz
Suppose the multiple slits from the previous
slide were illuminated with white light, instead
of red. What would the pattern on the screen look
like?

1. The three bright lines would be white, with a
   little colour at the edges, but otherwise the
   same
2. Each of the three lines would spread into a wide
   coloured spectrum
3. Two of the three lines would spread into a wide
   coloured spectrum, with the centre one narrow and
   white