(Solved): (11\%) Problem 8: A beam of light passes through a slab of glass as represented in the figure. The ...

(11\%) Problem 8: A beam of light passes through a slab of glass as represented in the figure. The index of refraction of the glass is \( n_{g}=1.5 \). The index of refraction of air is \( n_{\mathrm{a}}=1 \). The incident angle of the light is \( \theta_{i}=52^{\circ} \). (25\% Part (a) If the refraction angle of the light at the upper surface of the slab is \( \theta_{1} \), express \( \sin \theta_{1} \) in terms of \( \theta_{i}, r_{a} \), and \( n_{g} \). \( \sin \left(\theta_{1}\right)=n_{k} \sin \left(\theta_{1}\right) n_{k} \quad \vee \) Correct! \( 25 \% \) Part (b) The incident angle of the light on the lower surface of the slab is \( \theta_{2} \). What is the relation between \( \theta_{1} \) and \( \theta_{2} \) ? \( 0_{1}=0_{2} \vee \) Correct 25\% Part (c) The refraction angle of the light on the lower surface of the slab is \( \theta_{f} \). Express sia( \( \left.\theta_{f}\right) \) in terms of \( \theta_{2}, n_{a} \) and \( s_{f} \). \( \sin \left(\theta_{i}\right)=n_{k} \sin \left(0_{2}\right)_{n_{4}} \quad \vee \operatorname{Corredt} \) 8 \( 25 \% \) Part (d) What is the final angle \( \theta_{f} \) in degrces?