Wave nature of light problem

1. May 3, 2005

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 $$D * sin (\theta) = m \alpha$$ ?

2. May 3, 2005

OlderDan

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

3. May 3, 2005

leolaw

that sin of zero degrees is 0

4. May 4, 2005

OlderDan

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

$$D * sin (\theta) = m \alpha$$

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