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In Figure $($a$),$ a beam of light in material $1$ is incident on a boundary at an angle of ${}_1=30.$ The extent of refraction of the light into material $2$ depends, in part, on the index of refraction $n_2$ of material $2.$ Figure $($b$)$ gives the angle of refraction ${}_2$ versus $n_2$ for a range of possible $n_2$ values. The vertical axis scale is set by ${}_{2a}=15$ and ${}_{2b}=45.($a$)$ What is the index of refraction of material $1?($b$)$ If the incident angle is changed to $80$ and material $2$ has $n_2=2\mathrm{.}9,$ then what is angle ${}_2?$

$($a$)$

$($a$)$ Number $$

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$($b$)$ Number $$

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