I have performed experiments in my college laboratory on Newton's rings to find radius the of curvature of the convex lens used. I always get a dark center. Is it possible to get a bright center? If yes, how?
One can do this but it is difficult and you would need a great deal of patience and optical experimentation skill.
The reason that the centre is almost always dark is that the classic Newton's rings experiment simply involves putting the convex lens in contact with the reference optical flat. The lens touches the flat at the centre; therefore near the centre the two reflexions from the surface of the convex lens and from the flat are almost in phase. They are also opposite in sign, since one is from light going from glass to air (convex lens into the space), the other is from light going from air to glass.
What you would need to do for a non-dark centre, and indeed what you should do if you do not want to marr the convex lens's surface by the test, is to hold the two surfaces a half wavelength apart (at the centre). To do this, you would need to mount the flat or lens in a translation stage and bring the two surfaces together very carefully until the ring pattern can be seen. If you can do this successfully, you should be able to adjust for a bright centre.
By altering the lens flat plate distance it. Is certainly possible to get a bright ring area in the centre. Given the increasing that distance by a quarter (or three quarters etc) of the wavelength of light will produce bright ring means that you need a way of moving the lens very small distances.
Without such a device you might find a bit of dust between the lens and the flat plate and some trial and error (eg pressing the lens down) does the trick?
Another way of thinking about the central dark area is as follows.
Whenever there is a boundary some light is reflected.
Where the glass lens touches the glass plate underneath the lens there is not discontinuity in medium and so (almost) no reflection takes place, hence the dark centre.
Observation from the other side does produce a bright centre because (almost) all the light is transmitted.
The contrast for the Newton's rings seen by transmission is much worse than for those seen by reflection because for the transmitted light beam intensity is so much greater than the reflected beam. The interference is due to the overlap of light which suffers no reflection and light which suffers two reflections and so complete cancellation cannot happen.
In the conventional set up the interference is between light which has only suffered one reflection and so the cancellation (dark ring) can be almost complete.