In Youngs Double Slit Experiment why do we observe separate bright and dark bands? Shouldn't there be a continuous change from a maximum intensity to a minimum intensity (that is 0) and so on, so that we don't observe separate bright and dark bands?
It would be helpful, if you provided a reference or an image.
Yes, in principle we should observe a continuous change in the intensity. However, each sensor has a certain dynamical range: It can't resolve the continuous intensity. Therefore, the image will tend to become discretized. Just take a look at photographs, which are taken towards the sun.
In textbooks or on the Internet you see two types of images of the fringes.
Ones which have been produced in a painting application and they look too good to be true
others which are a genuine photographs (I think)
which are often characterised by over exposure in the centre (almost white blobs) to get a reasonable exposure for the higher order fringes.
Theoretically the intensity profile of double slit fringe pattern should look like this
where the intensity of the $\cos^2$ "interference" fringes is modulated by the single slit diffraction pattern produced by each of the slits.
The eye is much better than any camera at being able to processes a large range of intensities and so by looking at the fringes set up for real you will see that there is a gradation in intensity from one fringe to the next.