Electric Potential

1
Diffraction and Limits of Resolution
2
Diffraction through a circular aperture of
diameter D
? 1.22 ? /D
Image on Screen
Diameter D
Intensity
Because of diffraction, images formed by
perfect optics are fuzzy.
3
For a circular apertureThe angle q from the
centre to first dark ring (angular radius of
central spot) is
?1.22 ?/D radiansThis is useful in calculating
the limiting resolution of optical instruments
(microscopes or telescopes).The central spot
is sometimes called the Airy disk
4
Quiz
What would the central spot look like if white
light were used for the beam?

1. Blue in the centre and red around the edge
2. Red in the centre and blue around the edge
3. White in the centre and red around the edge

5

• Example Sodium light (589nm) is used to view
  objects under
• a microscope. If the aperture of the objective
  has a
• diameter of 0.9 cm,
• find the limiting angle of resolution (max
  resolution)
• if the space between the object and the objective
  lens is filled with water (n1.3), how is the
  resolution affected?

6
Example If the eye pupil is dilated to a
diameter of 5mm, what the minimum distance
between two point sources that the eye can
distinguish at a distance of 1km?
7

Resolution of two sources by a Telescope
A perfect telescope only magnifies the
diffraction pattern of the circular hole it
looks through.
angle 1.22 ? /D

D

Two stars (point sources at infinity)
Telescope lens/mirror
Image (perfect focus)
8
Rayleigh Criterion
Images are just resolved when the centre of one
pattern overlaps the first dark line of the other
pattern.
Not Resolved
Rayleigh Criterion
Resolved
9

Just resolved (or just not resolved)
x
x
When it comes to optics, size does matter !!!
10
R 200 m
Fleas, s 2mm apart, treated as point sources of
light
Find Minimum lens diameter to
resolve fleas. (?500nm 1/2000 mm)
11
Example The moon is 386,000 km away. a) What
is the smallest feature that you can resolve
with a pair of 80mm binoculars?b) What is
the smallest feature that you can resolve with a
10m telescope?
Assume ?500nm
12
Quiz
What other factors can affect the resolution of a
telescope?

1. atmospheric turbulence
2. steadiness of telescope/mount
3. smoothness of mirror/lens
4. all of the above

13
Quiz
Which telescope will have the best resolution
given the same size of optics (aperture size),
and neglecting the effect of the atmosphere?

1. Radio telescope
2. Optical telescope
3. X-ray telescope

14
The Sun
x-ray
Radio
Visible
15
How to increase telescope resolution?
2) We can use more than one mirror in a telescope
16
How to increase telescope resolution?
1) Build a larger telescope telescope
17
How to increase telescope resolution?
3) Put the telescope in space