## College Physics (7th Edition)

$alpha=90^{\circ}$ for any value of $\theta_{i1}$
Let PQRS is parallelogram. So, Angle PQR + Angle QRS = $180^{\circ}$ Therefore, $(\theta_{i1}+\theta_{r1})+(\theta_{i2}+\theta_{r2})=180^{\circ}$ or, $2\theta_{i1}+2\theta_{r2}=180^{\circ}$ $\theta_{i1}+\theta_{r2}=90^{\circ}$ or, $\theta_{i1}+alpha-\theta_{i1}=90^{\circ}$ Therefore, $alpha=90^{\circ}$ Hence, for $alpha=90^{\circ}$ and for any value of $\theta_{i1}$ the ray will reflect in the direction from where came i.e. parallel to the incident ray.