Diffraction TEXT ................Resolution TEXT

 

Diffraction is appreciable if the wavelength is of the same order of magnitude as the opening or bigger. However, if the wavelength is much smaller than the opening size diffraction is neglible

Intensity of the wave has a inverse square relationship. I=P/(4pi*r2) = Power/Surface area of a sphere.

Destructive interference takes place if bsinx = n(wavelength), n = 1, 2, 3, ... Since the angle x is typically small sinx = x. And x = wavelength/b. If the aperture is circular x = 1.22wavelength/b

HW. PG 265: 1-4. Be sure you can do the proof for single-slit.

DOUBLE SLIT:

Separation of bright fringes for light of wavelength lambda ...

Separation Distance of bright fringes: s = lambda*D/d.

D is the distance from the double slit to the screen and d is the separation of the slits.

For multiple slits or a diffraction grating

n*lambda = d[sin(theta)] ... n = "order" of maximum [0 for central max, 1 for first max on each side, etc.], d = separation of slits, theta = angle for interference maximum.

For diffraction gratings it is normal for N, the # of lines per mm, to be quoted. Use that value to find the spacing between lines (or slits) in meter, d = 1/N.

The effect of increasing the number of slits:

  1. Destructive interference close to all the maximums,
  2. Maximums are now narrower.
  3. Maximums are now more intense.

Parallel Thin Film

  • Phase changes. This is the inversion of a wave (phase change of 180) that CAN take place at a reflection interface. This happens when light is reflected back from an optically denser medium (great index of refraction).

Single Slit Diffraction

Rayleigh Criterion

Looking at the diffraction patterns created by the two: 2 objects can be just resolved if the central maximum of one pattern is formed at the first minimum of the other pattern.

 

In general it should be known that to resolve a small object of size s, the wavelength of light must be of the same order of magnitude as s or smaller.

HW. PG 270: 1-7.

Resolution