$7.(15$ points$)$ A glass rod of refractive index $\backslash ($ n$=1\mathrm{.}6\backslash )$ and diameter $\backslash ($ d$=1\mathrm{.}6\backslash$mathrm$\{$~cm$\}\backslash )$ has a hemispherical cap. There is a fault in the glass $\backslash (\backslash$ell$=2\mathrm{.}3\backslash$mathrm$\{$~cm$\}\backslash )$ from the end. Can you see this fault if you look at the rod through the spherical cap along the axis of symmetry? From about how far away should you look?