I was solving this question,

I arrived at the correct answer which is 'A' the reason 'C' and 'D' are incorrect is cuz the fringes would eventually converge as if we look at this question from another point of view it's similar to a light source striking a plano-convex lens (But the lens is cut out from a cylinder).

As an exercise I tried to find out the distance between the fringes produced by relating it with some variable that's changing with every fringe, which in my case was θ.

The text in pink says 'Interference between these 2 rays'.

I also found an article on Newton's Rings but I failed to understand how they arrived at the formula

$$r_N=\left[\lambda R\left(N-\frac{1}{2}\right)\right]^{1/2}$$

Could someone please help me out here, thank you!

I was solving this question,

I arrived at the correct answer which is 'A' the reason 'C' and 'D' are incorrect is cuz the fringes would eventually converge as if we look at this question from another point of view it's similar to a light source striking a plano-convex lens (But the lens is cut out from a cylinder).

As an exercise I tried to find out the distance between the fringes produced by relating it with some variable that's changing with every fringe, which in my case was θ.

The text in pink says 'Interference between these 2 rays'.

I also found an article on Newton's Rings but I failed to understand how they arrived at the formula

$$r_N=\left[\lambda R\left(N-\frac{1}{2}\right)\right]^{1/2}$$

Could someone please help me out here, thank you!

EDIT:-

The solution has been linked in the comments to this post please check it out.