Single-Slit Diffraction - Orange Coast...
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(a) The diffraction patterns of (a) a straight edge, (b) a small circular obstacle, and (c) a razor blade. In all three cases, plane waves fall on the diffracting obstacle and the diffraction pattern is observed on a screen placed behind and close to the obstacle. Chapter 42
Transcript of Single-Slit Diffraction - Orange Coast...
(a) The diffraction patterns of (a) a straight edge, (b) a small circular obstacle, and (c) a razor blade. In all three cases, plane waves fall on the diffracting obstacle and the diffraction pattern is observed on a screen placed behind and close to the obstacle.
Chapter 42
Accordingly, diffraction of waves depend on two factors:(a) The size of the wave determined by (wave length),(b) The size of the obstacle determined by a (dimension).
If light behaved as particles, one would not expect to have any light in the region of the geometric shadow of an opaque object!
Diffraction pattern produced when light passes through a narrow slit.
Single-Slit Diffraction
Generally, two converging lenses are used to achieve Fraunhofer diffraction condition, where both incoming and out going waves to the plane waves. The second lens, f2, is to focus on the emerging parallel rays.
Illustrating the conditions required forproducing minima in the first (m = 1)and second (m = 2) orders for a singleslit.
In general, one may divide the slit width “a” in to a/2 regions. If the path difference between any two rays is /2, then will combine to form destructive interference.As:
R2 as compared to R1 travels an extra distance of /2. Similarly, R3 moves /2 more than R2.
Condition for mth order minima
Hence:
For example: If = 650nm, the slit width “a” needed for the first order minimia to occur at 1 = 15, is:
Human hair is about:10m in diameter.
What wave length will have its first order maximum to fall on the first order minimum at 15 for “a” = 2.51m?As a general rule, a maxima occurs half way between minima. For maxima to be at 15, then must be a minima at 10 and a 2nd minima at 20 for the wave length .
The mth order diffraction minima is given by: a.sin=m, m = 1, 2, 3, …To find the intensity of light at a given point, we divide “a” into N equal strips of width x.Each x is narrow enough that all Hugens wavelets through each slit are in phase and that wavelets arriving at a point P from any two adjacent strips have constant phase given by:
