CAT $1$ BCH$2206$ Answer All questions

a$)$ Using Snell's law $({}_{1}sin{}_1={}_{2}sin{}_2)$ and the diagram below find the angular dispersion of the outgoing beam from the prism.

Given

$n_{\text{r}\text{e}\text{d}}=1\mathrm{.}582$

$n_{\text{v}\text{i}\text{o}\text{l}\text{e}\text{t}}=1\mathrm{.}633$

${}_i=45$

$(6$ marks$)$

b$)$ Explain how a photomultiplier detector works.

$(4$ marks$)$