Question

if the absolute refractive index of glass is 1.5 and that of water is 4/3 find the refractive index of water with respect to glass

Answer 1

$\bold{\boxed{Refractive\:index\:of\:water\:with\:respect\:to\:air}}$ = $\bold{\frac{4}{3}}$ (Given)

$\bold{\boxed{Refractive\:index\:of\:glass\:with\:respect\:to\:air}}$ = $\bold{\frac{3}{2}}$ (Given) (1.5 = $\bold{\frac{3}{2}})$

$\bold{\boxed{Refractive\:index\:of\:air\:with\:respect\:to\:water}}$ = $\bold{\boxed{\frac{1}{(Refractive\:index\:of\:water\:with\:respect\:to\:air)}}}$ = $\bold{\frac{1}{\frac{4}{3}}}$ = $\bold{\frac{3}{4}}$

$\bold{\boxed{Refractive\:index\:of\:glass\:with\:respect\:to\:water}}$ = (Refractive index of glass with respect to air) × (refractive index of air with respect to water)  = $\bold{\frac{3}{2}\times\frac{3}{4}\:=\:\frac{9}{8}}$

$\bold{\boxed{Refractive\:index\:of\:water\:with\:respect\:to\:glass}}$ = $\bold{\frac{1}{(Refractive\:index\:of\:glass\:with\:respect\:to\:water)}}$ =  $\bold{\frac{1}{\frac{9}{8}}}$ = $\bold{\frac{8}{9}}$

∴ Final required answer = $\bold{\frac{8}{9}}$

Thanks!