$(10$pt$)$Imagine the circlular cavity with the radius $R.$ Through the hole on the cavity$($point $O$ of the figure below.$),$ two laser beam with wavelength $$ are going inside. The beam$1$ is incident $30$ to the vertical direction, and the beam$2$ is incident $60.$ Assume that lasers are fully reflected at the inner wall of the cavity.

$($a$)$ If there is a destructive interference on point $A,$ what kind of interference $($constructive or destructive$)$ occurs at point $B$ and $O($by the outgoing waves$),$ respectively?

$($b$)$ What is the smallest possible radius of the cavity if the constructive interference has occured by the outgoing beams at $O?$