Answer
34 bright rings are formed.
Work Step by Step
From the previous problem, we have the expression for the radii of the rings:
$r=\sqrt{(m+{1\over 2})\lambda R}$
Solving this for $m$,
\begin{align*}
r^2&=\left(m+{1\over 2}\right)\lambda R\\
{r^2\over \lambda R}&=\left(m+{1\over 2}\right)\\
m&={r^2\over \lambda R}-{1\over 2}\\
\end{align*}
Substituting the given values, $r=10\times 10^{-3} \mathrm{m}$, $R=5.0 \mathrm{m}$ and $\lambda=589\times 10^{-9}\mathrm{m}$, we get
\begin{align*}
m&={(10\times 10^{-3})^2\over 589\times 10^{-9}\times 5.0}-0.5\\
&=33.4
\end{align*}
Since $m=0$ is the first bright ring, there are a total of 34 bright rings formed.
