All I got was two parallel bright fringes instead, like the ones you would get by shining a torch through two very thick slits.
It means the separation between slit is not close and the slits size is not small enough! Those two light beam must overlap to have interference. Small slit size is required to have large diffraction, the optimal slit size is certainly small than wavelength $\lesssim\lambda\approx0.5\mu m$ which gives you large diffraction. However, larger slits size is ok, but you have to (a) Make two slits as close as possible (b) move the setup far from the screen. You will know that it is enough when the light beam can overlap.
For the slit, you need better tools than a knife as well as a better material. First, you should use a shape cutter. Second, you need a material that can have a sharper edge such as film. I believe that film was used in the first few experiments of this kind. You have mentioned a hair is enough so $10\mu m$ should probably be ok, you just need to move the screen further away.
For the light source, you should always use a laser, since a high coherent light is required. Any laser out there is ok, it just cost 1 dollar and I can sure you can borrow a laser pointer near you. As I remember when I was doing Michelson Morley experiment, a tungsten light only gives interference pattern for $<0.1m$ with short coherent length, but a laser can have coherent length $>2m$. It means your life can be easier as you can use a 20 times larger slit with a laser!
Edit: Additional info on the methods Young used for this experiment.
The wiki about Young' interference experiment has quoted his paper on "On the nature of light and colours" (Also around page p.140 in the book Method and Appraisal in the Physical Sciences). The relevant excerpt is:
In order that the effects of two portions of light may be thus combined, it is necessary that they be derived from the same origin, and that they arrive at the same point by different paths, in directions not much deviating from each other. This deviation may be produced in one or both of the portions by diffraction, by reflection, by refraction, or by any of these effects combined; but the simplest case appears to be, when a beam of homogeneous light falls on a screen in which there are two very small holes or slits, which may be considered as centres of divergence, from whence the light is diffracted in every direction.
So, I guess the experiments were carried out as follow:
- Light source: In a room with all windows covered with thick curtains so that the inside is completely dark. Then let a small beam of sunlight go in.
- Monochromatic light: Use prism to split light into different color (This is known method back to Netwon). To get high quality single frequency light, a slit is required in front of prism to get a narrow sunlight beam.
- Point source of monochromatic light: Add another slit to get the required color (S1 in Fig. 1), the output monochromatic light is therefore from a single point source.
- Interference: Add another double slits (S2 in Fig. 1) so that the light can have two different path. Make sure that light from S1 falls on the slits S2. To ease observations, the screen should be far away.
Since his results cover all color, so it is very likely that he used sunlight rather than other light source such as candle (There was no light bulk at that time). Also, there is no diffraction grating, so it is likely that he was just using a simple prism.
For home experiments carried out these day, we can use LED as a monochromatic light source so that step 1 and 2 can be skipped. If you use a torch, you still need the step 2.
I hope the following diagram is a "picture worth more than a thousand words":
As you can see, a "narrow" first slit gives all the light incident on the pair of slits a very definite direction - and therefore a very definite location of the fringe pattern.
When the first slit is wider, the light could be hitting the double slits in multiple different directions. Each direction gives rise to its own fringe pattern; the sum of these patterns is a pattern with reduced contrast.
Best Answer
The separation of the interference pattern fringes does not depend on the width of the slits.
Each slit produces its own diffraction pattern.
As the slit gets wider the diffraction pattern gets narrower. Where the two diffraction patterns overlap you get the interference pattern.
When the slits are narrow the diffraction spreads the light out and there is considerable overlap of the diffraction patterns and hence there are many fringes visible.
With wide slits and narrow diffraction patterns the light does not spread out as much and so the amount of overlap of the diffraction patterns is less so there are fewer fringes visible.
Later
The diagrams from the HyperPhysics website are excellent and I have copied two of them to illustrate the effect of changing the slit width.
The diagram on the left shows the diffraction pattern due to a single slit.
The width of that pattern is controlled by the slit width.
In the double slit arrangement the diffraction patterns from each slit overlap and an interference pattern is produced whose intensity is modulated the by diffraction pattern due to a single slit.
The separation of the interference fringes depends on the slit separation.
If now the slit width is increased the width of the diffraction envelope is decreased whilst the separation of the interference fringes stays the same.
So less interference fringes will be visible.
Below the two diagrams there are a pair of photographs from the University of New South Wales website which illustrate the effect quite well and all you need to do is imagine what you would see if the diffraction envelope decreased in width.