Consider a light ray traveling between air and a diamond cut in the shape shown in the figure below. $($Assume $=36\mathrm{.}6.)$

$(1)$

$($a$)$ Find the critical angle for total internal reflection for light in the diamond incident on the interface between the diamond and the outside air.

$q,$

$($b$)$ Consider the light ray incident normally on the top surface of the diamond as shown in the figure. Show that the lioht travelinn toward noint $D$ in the diamnnd is totally reflected.

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$($c$)$ If the diamond is immersed in water, find the critical angle at the diamond$-$water interface.

$($d$)$ When the diamond is immersed in water, does the light ray entering the top surface in the figure undergo total internal reflection at $P?$

Yes

No

Explain.

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$($e$)$ If the light ray entering the diamond remains vertical as shown in the figure, which way should the diamond in the water be rotated about an axis perpendicular to the page through $O$ so that light will exit the diamond at $P?$

clockwise

counterclockwise