Let there be light

Because light travels slower through glass than through air, then according to Snell's law:

$\large\frac{\sin \alpha_{air}}{\sin \alpha_{glass}} = \frac{n_{glass}}{n_{air}} = n$ .

The rays impact on the glass under the angles of interval $\langle\ang{0}, \ang{45}\rangle$ .

So after breaking they will impact under the angles in $\langle\ang{0}, \arcsin [\frac{\sin(\ang{45})}{n}]\rangle \approx \langle\ang{0}, \ang{28.1}\rangle$ .

Therefore the total part of the illuminated universe (on 4 sides under degrees $\langle\ang{-28.1}, \ang{28.1}\rangle$ will be:

$4\frac{2 \times \ang{28.1}}{\ang{360}} = \boxed{0.625}$