** **

**What is Diffraction?**

Diffraction
is the deviation of a wave from its *straight ray propagation*. This occurs when part of the wave is
obstructed by a boundary. Diffraction
is a **wave phenomenon** so light undergoes diffraction because of its wave
nature.

** **

**Why does it occur?**

In
accordance with *Huygen’s
Principle* as a wave from a single source propagates through space
each *wavefront*
can be thought of as consisting of numerous individual secondary wavefronts. Diffraction occurs because part of the wave
(some of the secondary wavelets) that is obstructed changes phase or amplitude
and interferes with the rest of the unaltered wave (the rest of the secondary
wavelets). This causes multiple **interference**
patterns resulting in the diffraction of the wave.

** **

**What affects the diffractive behavior
of a light source at a boundary? **

-The
**wavelength** of the light source

-The
distance from **light source** to the **boundary**

-The
distance from the **boundary** to the **screen **where the diffraction
pattern is projected

-The
size, shape, and nature of the boundary or the obstruction

** **

**What are the conditions for Fresnel
Diffraction? **

Fresnel
diffraction occurs when either the **distance**
from the source to the obstruction or the distance from the obstruction to the
screen is **comparable **to the **size** of the obstruction. These comparable distances and sizes lead to
unique diffractive behavior.

**Why is Fresnel Diffraction different
than other types of diffraction? **

The
approximations made for *Fraunhofer Diffraction* are no longer
valid. The light source can no longer
be considered a planar wavefront at the aperture because it can longer be
approximated to originate at infinity.
It must be considered a **spherical wavefront**.

-The
*relative phase
difference* for a curved wavefront is **not constant**.

-Amplitudes
of the individual light waves (secondary wavefronts) at the observation point
are not equal because the distances traveled by each element, or wavefront, can
no longer be considered approximately equal.
Therefore, the *intensity *of light on the screen varies from
point to point.

** **

**How is Fresnel Diffraction dealt with
mathematically?**

-All
parameters (lengths, distances, widths, etc.) must be considered in the
mathematical interpretation of Fresnel diffraction because of their comparable
sizes.

-One
can determine the diffraction pattern caused by Fresnel diffraction by
determining the intensity of light at each point on the viewing screen.

a b

The intensity at each point
on the screen can be determined by a parameter **V**

**V
= v _{1 - }v_{2}**

where

**v _{1}
= [s/2 + k][2(a +b)/ab(wavelength))]^{1/2}**

** v _{2} = [-s/2 + k][2(a +b)/ab(wavelength))]^{1/2}**

and

**k** depends on **q** (the distance from the center of the screen
to the point (x,y) on the screen where you wish to determine the intensity)

**v _{1 }**and

therefore
there is a unique V for every point on the screen and its value
determines the intensity at that point

** **

**How is
Fresnel Diffraction represented graphically?**

This parameter V and, therefore the resultant Fresnel diffraction pattern, can be represented graphically as well.

The
**resultant amplitude** (intensity) of light at an observation point can be
determined by **vectorially adding** (head to tail) each of the individual
amplitude components.

For **Fraunhofer** diffraction, where the **relative phase** of these elements is **constant**, the vector addition simply
gives an arc length of a circle and the intensity is the cord length of that
arc.

**Fresnel** diffraction introduces **another phase shift **due to the curvature of the wave. Therefore, each consecutive amplitude is
longer displaced the same amount (forming a circular arc length) rather these
elements bend into a spiral curve.

**What
is a Cornu Spiral?**

The
Cornu Spiral is the geometric depiction of the Fresnel diffraction patterns due
to different barriers. Each point on
the spiral has a value that corresponds to certain **v _{1}(k)_{ }**or

**How do different barriers and apertures
affect the diffraction pattern?**

One can see from the graph above that the **cord
length** between two points determines the **intensity **of the pattern **produced
on the screen**. Because the bottom
half of the **barrier extends to infinity**, **v _{1} **always has an

**single slit**
is similar to that of **Fraunhofer diffraction** except the areas of minimum
intensity do not go to zero (i.e. there is never complete destructive
interference)

The
diffraction pattern due to an opaque circle is identical to that of a
circular aperture except for the bright spot in the center of the
pattern. The mathematics of
Fresnel's theory and the Cornu Spiral predict this bright spot but it is
often very hard to see. Poisson
actually tried to argue that Fresnel's theory was wrong because it
predicted such a spot that had not been found experimentally. This spot is now often referred to as |

References

Dauger,
Dean. Fresnel Diffraction. http://www.dauger.com/fresnel/

Weisstein,
Eric. Fresnel Diffraction - from Eric's Wonderful World of Physics. http://scienceworld.wolfram.com/physics/FresnelDiffraction.html

Fresnel
Diffraction. http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/fresnelcon.html

Hecht,
Eugene. Optics 4ed. Addison Wesley, San Francisco : 2002.