Light passes from air into a liquid and is deviated $22$ from its initial path when the angle of incidence is $64.$ What is the index of refraction for the liquid? The index of refraction for the air is $1\mathrm{.}00.$

Hint: Think carefully about what the word "deviated" means.

$($a$)1\mathrm{.}34$

$(2)1\mathrm{.}56$

$($&$)1\mathrm{.}76$

$($d$)1\mathrm{.}81$

$($e$)2\mathrm{.}40$