When does the single slit diffraction formula apply?

[PhiJ]

When do single slit diffraction patterns occur (i.e. when is the formula sin(theta)=(lamda)/b applicable)? Is it only when the light gets put through a lens and focused on a single point at different angles, or is it generally. My textbook derives it for when the light is focussed, but my teachers presentation says that it is for if you just show the light on the screen without focussing it.
If this is true, could somebody derive it for me please?

Thanks, PhiJ

 

[marlon]

When do single slit diffraction patterns occur (i.e. when is the formula sin(theta)=(lamda)/b applicable)? Is it only when the light gets put through a lens and focused on a single point at different angles, or is it generally. My textbook derives it for when the light is focussed, but my teachers presentation says that it is for if you just show the light on the screen without focussing it.
If this is true, could somebody derive it for me please?
Thanks, PhiJ

diffraction occurs when the magnitude of the wavelength of the incident wave, is bigger then the magnitude of the opening (ie the slit).

marlon

 

[dextercioby]

There's no discussion over "focussing" in modern texts treating diffraction whatsoever.

Daniel.

 

[PhiJ]

But WHY do you get PATTERNS from a single slit?

btw, how do you do greek on this forum, do you just have to copy it from word?

 

[Integral]

For Greek letters and equations read https://www.physicsforums.com/showthread.php?t=8997"

 

[Claude Bile]

Fraunhofer diffraction theory assumes a planar incident wave. One way of obtaining a planar incident wave is by focusing the light and placing the aperture at the focus. The theory of Gaussian beams tells us that the curvature of the field is exactly zero at the focus. The advantage of using this method is that a brighter diffraction pattern will be obtained.

A second way of acheiving a planar wavefront is by simply collimating the beam (i.e. focusing at a distant object). The advantage of using this method is that the placement of the aperture is not critical since the curvature of the wavefront is close to zero along the length of the collimated beam.

So essentially the textbook and your teacher are describing two different methods of achieving a planar wavefront. In summary, how you obtain the planar wavefront is not critical. Both methods can be used with success to obtain a Fraunhofer diffraction pattern.

Claude.

 

[marlon]

But WHY do you get PATTERNS from a single slit?
btw, how do you do greek on this forum, do you just have to copy it from word?

in an very easy/intuitive language, you get patterns because when the wave passes through the slit, it gets a pathlength difference between the parts of the wave at the top and bottom of the slit (ie different distances to be crossed if you want them to come together at the same point). This leads to interference between the different "parts" of the wave.

You see ?

marlon

 

[PhiJ]

But the patterns you get at the other end of the slit, why does the intensity of light reach a zero and then increase again afterwards?

 

[marlon]

But the patterns you get at the other end of the slit, why does the intensity of light reach a zero and then increase again afterwards?

that is the transition from constructive to destructive interference and back.

see this

marlon

 

[PhiJ]

Nearly get it. Can waves travel in bendy lines, or only straight?

 

[marlon]

Nearly get it. Can waves travel in bendy lines, or only straight?

err, what exactly do you mean ?

If you are talking about changing direction, the wave does not do this "automatically".

In particle language, photons can 'change" in absorption/emission phenomena , if the incident dirction of the absorbed photon is different from the direction of the emitted photon. Keep in mind that these are not the same hoton, though. A photon itself does always follow a straight line because it's resmass is 0.

marlon

 

[PhiJ]

Thanks, I get it now.

 

[PhiJ]

Wait... Why can the wave turn the corner when diffracted. Do we just have to say 'it does' or is there an explanation?

 

[Claude Bile]

There is an explanation - Maxwell's equations. Every electromagnetic phenomenon is derived from them, including optical phenomenon.

A good description of what happens to wavefronts as it passes through the aperture is described by Huygen's principle.

Claude.