A solid glass sphere of refractive index n=sq | vedclass

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(C) For the light to be fully polarized upon reflection,the angle of incidence at the inner surface must be the Brewster's angle,$\alpha$. According t

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$0.75$

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(C) For the light to be fully polarized upon reflection,the angle of incidence at the inner surface must be the Brewster's angle,$\alpha$. According to Brewster's law,$	an \alpha = \frac{n_{glass}}{n_{air}} = \frac{\sqrt{3}}{1} = \sqrt{3}$.Thus,$\alpha = 60^{\circ}$.Let $\beta$ be the angle of refraction at the inner surface. By Snell's law,$n_{glass} \sin \beta = n_{air} \sin \alpha$,so $\sqrt{3} \sin \beta = 1 	imes \sin 60^{\circ} = \frac{\sqrt{3}}{2}$,which gives $\sin \beta = 0.5$,so $\beta = 30^{\circ}$.In the triangle formed by the center of the sphere,the center of the cavity,and the point $O$,the sides are $R/2$,$R/2$,and the distance from the center of the sphere to $O$ is $R/2$. Using the sine rule in the triangle with sides $R/2$ and $R/2$ and angle $\beta=30^{\circ}$,we find the geometry leads to $\sin 	heta = \frac{3}{4} = 0.75$.

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