On the relationship between slit width and light diffraction In a light diffraction experiment, using a laser and a diffraction grid we can observe that the slits produce a diffraction pattern when the light from the laser goes through it. I have the hypothesis that the slits need to be equal or smaller than the light wavelengths in order for diffraction to occur. Is this true? If not, why is it that as wider slits are used less diffraction is observed? Is there any other factor I am missing?
The setup looks like this:

 A: The equation for a transmission diffraction grating with light at normal incidence is as follows (from Diffraction Grating Tutorial):
$$m\lambda=asin(\theta_m)$$
where m = 1, 2, 3..., $\lambda$ is the wavelength of light, a is the slit spacing and $\theta_m$ is the transmitted light angle from the normal to the grating. Let's consider just the first order, m = 1.
So sin($\theta_m$) = $\lambda$/a and as the sine function is at most equal to 1 (which corresponds to the most diffraction) we have
$$\lambda/a \le 1$$ $$a \ge\lambda$$
So in fact the slit spacing must be equal to or greater than the wavelength of light. The maximum diffraction occurs when a = $\lambda$, that is, the wavelength of light is equal to the slit spacing. At smaller wavelengths for a given spacing, or larger spacing for a given wavelength, the diffraction is less.
A: If the slits are too small the light will not pass, if the slits are just big enough the pattern is very wide and the intensity is low, which is difficult to measure.  So the slits are large enough to give good visibility of both the diffraction and the "interference".
Another way to study diffraction is with a camera lens where you can make the aperture small, when you image a small object that should only illuminate a few certain pixels you will find the adjacent pixels also get some signal .... you can wiki "Airy Disk".
A: There are two issues here: the width $w$ of the individual slits  and the distance $d$ between the centre of one slit and the next. The physical phenomenon called 'diffraction' refers to the fact that after passing through any narrow slit, the light spreads out from there. This can be observed for any value of $w$. The spreading can be indicated by the angle $\alpha$ between the direction of propagation of the light at one side and the light at the other side of the diffracting beam. This is not a precise quantity because the beam intensity does not fall to zero abruptly, but when $w > \lambda$ it is given roughly by
$$
\sin (\alpha/2) \simeq \frac{\lambda}{w}.
$$
For $w < \lambda$ one just gets $\alpha \simeq \pi$ radians, which just means the light spreads out in all directions when it passes through a slit of width less than one wavelength. For $w > \lambda$ you still get diffraction, just not as much. Even a wide opening, with a width of many wavelengths, produces some diffraction, and this is important in practice because it limits the resolution of optical instruments such as telescopes and spectrometers. A good rule-of-thumb for a telescope is that the angular blurring owing to diffraction is approximately $\lambda/w$ where $w$ is the width of the first lens (called the objective lens).
The other important formula for diffraction gratings, and the one which is usually mentioned first, is for the directions where there is constructive interference of the light emerging from all the slits. For a collimated beam at normal incidence this happens when
$$
d \sin \theta = m \lambda
$$
where $m$ is an integer and $\theta$ is the direction of propagation after the grating. The case $m=0$ leads to the solution $\theta = 0$ for any wavelength. This says that some light simply passes straight on without changing direction. The case $m=1$ is called the '1st order' and the formula gives the angle
$$
\theta = \sin^{-1} ( \lambda / d ).
$$
When $d > \lambda$ this gives the angle of the first order beam of given wavelength. When $d < \lambda$ there is no solution. This tells you that there is no 1st order (or any higher orders) when the slits are separated by less than one wavelength. In this case there is only the straight-through beam ($m=0$) called 'zeroth order'.
The case $d < \lambda$ implies $w < \lambda$ since we must have $w < d$.
In practice $d < \lambda$ is not a good choice for a diffraction grating, because we usually want to use the grating to steer the light through an angle which depends on wavelength. That is how the grating is used for spectroscopy, for instance.
(By the way, in practice diffraction gratings are normally used in reflection rather than transmission, and there is a clever way to make a reflection grating such that $w$ is almost equal to $d$. This is good because it maximizes the intensity of the reflected light for any given value of $d$. But in this case another feature has to be designed in, called 'blazing', which I will not get into here.)
A: It has nothing to do with the slits or their width. Diffraction occurs at single edges. A slit is nothing more than two separate edges. Each edge creates its own diffraction pattern on the screen, and the closer the edges are to each other the more the two patterns overlap. The further the edges are away from each other the less they overlap. Like any Moire Pattern https://en.m.wikipedia.org/wiki/Moir%C3%A9_pattern this changes the final pattern.  Also with a wider slit, more light hits the screen and overwhelms the patterns that are there.
