The X-Z plane separates two media A and B of refractive indices ${\mathrm{\mu }}_{\mathrm{A}}\equiv 1\text{.5 and }{\mathrm{\mu }}_{\mathrm{B}}\equiv 2$ . A ray of light travels from A to B, its direction in two media are given by unit vectors.${\widehat{\mathrm{u}}}_{\mathrm{A}}=\mathrm{ai}+\mathrm{bj}$ and ${\widehat{\mathrm{u}}}_{\mathrm{B}}=\widehat{\mathrm{ci}}+\mathrm{dj}$ respectively, then