The data on a CD is stored as a series of pits in a spiral track on a metal information layer $($see figure $($a$)$ below$).$ Affixed to this layer is a layer of polycarbonate plastic with a thickness of $t=1\mathrm{.}20mm$ and an index of refraction of $n=1\mathrm{.}55($see figure $($b$)$ below$).$ A laser beam enters this plastic layer from below and is refracted to a width of $a=1\mathrm{.}60m$ in order to read the data on a single track. A lens makes the beam converge into a cone with an apex angle $2{}_1$ before it enters the plastic layer, and its width as it enters the layer is $w=0\mathrm{.}750mm.$ What is the incidence angle ${}_1($in degrees$)$ of the light at the edge of the conical beam?

$($i$)$

$($i$)$

From the figure, how is the angle ${}_2$ related to $t$ and $b?$ How is $b$ related to $w$ and $a?$ From Snell's law, how is ${}_1$ related to ${}_2?$