Diffraction

define diffraction (2)

• when a wave hits an obstacle, it bends around the obstacle

• same effect at a hole - wave spreads out around the other side of the hole

give an example of diffraction

water

explain Huygens principle of secondary wavelets (3)

• starting from a known point - every point on a wavefront is a source of wavelets

• the wavelets spread out in a spherical forward direction at the same speed (as the original wave)

• the new wavefront is tangent to all the wavelets

State the Fresnel-Huygen principle of secondary wavelets (2)

• Every point on a wavefront acts as a secondary source of a spherical wavefront of the same frequency

• The magnitude of the displacement at any point beyond is the superposition of all the secondary wavelets at that point having regard for their amplitudes and relative phases

compare and contrast Fresnel and Fraunhofer diffraction patterns (3)

• Fresnel - the source of light and screen is at a finite distance from the object - near-field - near object point WHEREAS Fraunhofer - source of light and scree is at an infinite distance from the obstacle - far field - distant observation point

• Fresnel - observed anywhere in the diffracted beam apart for the in-focus image plane WHEREAS Fraunhofer - observed in the in-focus image plane of a source

• Fraunhofer - important in optical systems including the eye

how can Fraunhofer’s diffraction be demonstrated

through a single slit experiment

explain the above experiment (2)

• Adjustable slit is placed on the table of a spectroscope and a monochromatic light source is
  viewed through it using the spectroscope telescope.
  • Slit is narrowed a broad diffraction pattern spreads out either side of the slit, only disappearing when
  the width of the slit is equal to or less than 1 wavelength of the light used

why are circular aperture diffraction patterns important

most optical instruemnts including the eye have circular apertures

in a lens system corrected for abberation the detial in an image is limitd by diffraction - unwantd spread of light as it passes through pupil affects sharpness of image

explain the circular aperture diffraction patterns in the eye and why it is important

• most optical instruments including the eye have circular apertures

• when light passes through these circular apertures (pupil) it does not form a perfect point image but instead spreads out into a pattern called an Airy disk.

• The size of this diffraction pattern determines the resolution limit of optical systems, affecting how well we can distinguish two closely spaced objects.

explain in more detail what an airy disk is (2)

• The amplitude distribution for
  diffraction due to a circular aperture
  forms an intensity pattern with a
  bright central circular area
  surrounded by concentric circular
  bands of rapidly decreasing intensity - ( Airy Disc) .
  • 84 % of the light arrives within the
  central peak called Airy disc.

explain resolution in imaging systems and its limits (5)

• imaging systems have a limit on determining detail in the image

• the closer the object points are the closer are their images are in the image plane of the optical system

• a - images are easily observed as separate images

• b - slight overlap

• c- complete overlap - no longer able to distinguish as two separate images

state rayleigh’s criterion - for the diffraction limit to resolution

Rayleigh Criterion for the diffraction limit to
resolution states that:

• 2 images are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other

what is the calculation / formula used to calculate this

θ=1.22 x λ / D
λ is the wavelength of light

D (m) is the diameter of the
aperture

θ is in radian

re-arranged: d = 1.22 x λ / 0