<image>Translate the following math problem with the  identifier retained in the text:

 Two right-angled coordinate planes $$\alpha$$ and $$\beta$$ with a common $$y$$-axis form a dihedral angle $$\alpha-y$$ axis $$-\beta$$ that equals $$60^{\circ}$$. Given that the equation of curve $$C'$$ within $$\beta$$ is $$y^{2}=4x'$$, and the projection of curve $$C'$$ within $$\alpha$$ results in the equation $$y^{2}=2px$$ on plane $$\alpha$$, find the value of $$p=$$ ______ .