There is a more elementary way.
<br />
n \propto L<br />
means that n increases with increasing L, while
<br />
n \propto d^{-4}<br />
means that n decreases with increasing d.
Therefore, the smallest value for n is obtained by taking the smallest value for L and the largest value for d:
<br />
n_{\mathrm{min}} = A \, \frac{L_{\mathrm{min}}}{d^{4}_{\mathrm{max}}}<br />
The largest value for n, on the other hand, is obtained by taking the largest value for L and the smallest value for d:
<br />
n_{\mathrm{max}} = A \, \frac{L_{\mathrm{max}}}{d^{4}_{\mathrm{min}}}<br />
In this way, you obtain an interval for the possible values of n:
<br />
n \in [n_{\mathrm{min}}, n_{\mathrm{max}}]<br />
Instead of the interval notation, one usually uses the "techincal notation":
<br />
n = \bar{n} \pm \Delta n<br />
which actually means:
<br />
\left\{\begin{array}{l}<br />
n_{\mathrm{min}} = \bar{n} - \Delta n \\<br />
<br />
n_{\mathrm{max}} = \bar{n} + \Delta n<br />
\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}<br />
\bar{n} = \frac{1}{2} \, (n_{\mathrm{min}} + n_{\mathrm{max}}) \\<br />
<br />
\bar{n} = \frac{1}{2} \, (n_{\mathrm{max}} - n_{\mathrm{min}}) \\<br />
\end{array}\right.<br />
Then, of course, the relative uncertainty, expressed in percent, is defined as:
<br />
\delta_{n} \equiv \frac{\Delta n}{\bar{n}} \cdot 100\%<br />
It is up to you to:
1. Find Lmin and Lmax by knowing \bar{L} (the nominal value) and \Delta L = \delta_{L}/{100 \%} \, \bar{L} (the absolute uncertainty);
2. Do the same for dmin and dmax;
3. Find nmin and nmax according to the above formulas;
4. Find \bar{n} (nominal value) and \Delta n (absolute uncertainty) according to the above formulas;
5. Find the relative uncertainty \delta_{n}.
