Maximum Width of Single Slit for No Diffraction Minima?

[leolaw]

Given a wavelength length \alpha, what is the maximum Width (D) of a single slit, which would have no diffraction minima?

It seems like a proof problem to me and I am trying to get a head start.
should I use D * sin (\theta) = m \alpha ?

 

[OlderDan]

Given a wavelength length \alpha, what is the maximum Width (D) of a single slit, which would have no diffraction minima?

It seems like a proof problem to me and I am trying to get a head start.
should I use D * sin (\theta) = m \alpha ?

Yes, that and what you know about the sine function.

 

[leolaw]

that sin of zero degrees is 0

 

[OlderDan]

that sin of zero degrees is 0

Yes, but at zero degrees you will never have a minimum. From the geometry of the single slit diffraction setup, to not find any minima after the slit, the angle \theta would have to be 90 degrees for the first minimum. So then what does

D * sin (\theta) = m \alpha

tell you about D?

 

[leolaw]

I see, so D sin (90) = (1) \alpha, which is the first minimum, and D has to be equal to the wavelength \alpha.