Answer
$1.4$
Work Step by Step
We can find the required index of refraction of the varnish as follows:
$tan\theta_B=\frac{n_2}{n_1}$
This can be rearranged as follows:
$n_2=n_1tan\theta_B$
We plug in the known values to obtain:
$n_2=(1.00)tan55^{\circ}=1.4$