Refractive index, not indices

$By\quad using\quad the\quad fact\quad that\\ { _{ 1 }{ \eta }_{ 2 } }\times { _{ 2 }{ \eta }_{ 1 } }=1\\ \therefore { _{ 2 }{ \eta }_{ 1 } }=1/{ _{ 1 }{ \eta }_{ 2 } }\\ Substituting\quad the\quad value\quad in\quad the\quad given\quad equation\\ { _{ 1 }{ \eta }_{ 2 } }+1/{ _{ 1 }{ \eta }_{ 2 } }=25/12\\ \therefore { _{ 1 }{ \eta }_{ 2 } }=4/3\quad or{ _{ 1 }{ \eta }_{ 2 } }=3/4\\ but\quad it\quad cannot\quad be\quad 3/4\quad \because \quad { _{ 1 }{ \eta }_{ 2 } }\quad becomes\quad less\quad than\quad { _{ 2 }{ \eta }_{ 1 } }\\ but\quad { _{ 1 }{ \eta }_{ 2 } }>{ _{ 2 }{ \eta }_{ 1 } }\\ \therefore \quad { _{ 1 }{ \eta }_{ 2 } }=4/3$