Question

how is the principle of newtons rings used to determine the optical flatness of a glass surface

Answer 1

 Turn on the sodium lamp. 

b Place the plano convex lens on the plain glass plate with curved surface in contact with the glass plate and place this system inside a reflector located under a travelling microscope. 
 
c Use a reflector to direct light onto the optical system. Adjust the inclination of the reflector to get maximum brightness (or the height of the lamp). 
 
d Focus the travelling microscope to see the bright and dark circular fringes (Newton's rings). 
 
e Carefully insert the thin film (say a paper strip), of thickness t, between the plano convex lens and the plane glass plate until the paper stops moving (see the diagram). 
 
f Now look through the microscope. Start from the central dark spot and count the number of dark fringes (or bright fringes) to the fringe that is adjacent to the thin film. Generally for ordinary paper samples, the number of fringes are of the order of 175 to 230. Patience is needed! 
 
g 
For dark fringes. 
Destructive interference occurs when the path difference, 2t = nλ , where λ = wavelength and n is an integer. 
This simplifies to t = (nλ)/2 
 
For bright fringes 
Constructive interference occurs when the path difference, 2t = (n + 1/2)λ, which simplifies to t = (2n - 1)λ/4.