Optics Newton’s ring apparatus Problem

[roam]

Homework Statement

Here is a worked problem:

A Newton’s ring apparatus is illuminated by light with two wavelength components. One of
these wavelengths is 546 nm. If the 11th bright ring of the 546 nm fringe coincides with the
10th ring of the other wavelength, what is the second wavelength? The spherical surface
has a radius of 1 m.

Solution:

Radius of m^th bright ring is:

$x = ((m-\frac{1}{2})\lambda R)^{1/2}$

So

$(10.5 \times 546 \times 10^{-9} \times 1)^{1/2} = (9.5 \times \lambda \times 1)^{1/2}$

$\lambda = 603.5 \ nm$

I don't see why they've used "m-1/2" instead of "m+1/2"?

Homework Equations

According to my textbook the radius of m^th bright fringe is:

$x = ((m+\frac{1}{2})\lambda R)^{1/2}$

Where R is the radius of curvature of the convex lens.

The Attempt at a Solution

My textbook always uses "m+1/2" whereas my lecture notes always use "m-1/2". I'm confused because id I use the first one I get an entirely different answer.

I would appreciate it if anyone could explain why we need to use the minus for this particular problem, and not the plus.

 

[jedishrfu]

Could there be a difference in how m is defined like is the very first ring m=0 or is it m=1

that is do they start counting at ZERO or at ONE?

 

[roam]

Thank you. I think if we start counting at $m=0$, we should use $m+\frac{1}{2}$. And if we count from $m=1$ then we should use $m- \frac{1}{2}$.

BUT what if the problem asked for minima, instead of maxima?

I mean, the condition for minima is $m \lambda$. Here do we count from m=0, or from m=1??