Diffraction

Diffraction is a phenomena that occurs when light encounters an obstacle. The waves of light can either bend around the obstacle, or in the case of a slit, can travel through the slits. The resulting diffraction pattern will show areas of constructive interference, where two waves interact in phase, and destructive interference, where two waves interact out of phase. Calculation of the phase difference can be explained by examining Figure 1 below.

In the figure below, two parallel waves, BD and AH are striking a gradient at an angle θo

. The incident wave BD travels farther than AH by a distance of CD before reaching the gradient. The scattered wave (depicted below the gradient) HF, travels father than the scattered wave DE by a distance of HG. So the total path difference between path AHGF and BCDE is CD - HG. To observe a wave of high intensity (one created through constructive interference), the difference CD - HG must equal to an integer number of wavelengths to be observed at the angle psi, CD−HG=nλ, where λ

is the wavelength of the light. Applying some basic trigonometric properties, the following two equations can be shown about the lines:

CD=xcos(θo)

and

HG=xcos(θ)

where x  is the distance between the points where the diffraction repeats. Combining the two equations,