Question

If the refractive index of second medium with respect to first medium is `" "_(2)n_(1)` and that of third medium with respect to second medium is `" "_(3)n_(2)` . What and how much is `" "_(3)n_(1)` ?

Answer 1

Refractive index of `2^(nd)` medium w.r.t `1^(st)`.
`" "_(2)n_(1)=(V_(1))/(V_(2)) `…………….(i)
Refractive index of `3^(rd)` medium w.r.t. `2^(nd)`.
`" "_(3)n_(2)=(V_(2))/(V_(3))` ……………(ii)
Similarly,
`" "_(3)n_(1)=` refractive index of `3^(rd)` medium w.r.t. `1^(st)`.
`" "_(3)n_(1)=(V_(1))/(V_(3))xx(V_(2))/(V_(2))`
`=(V_(2))/(V_(3)) xx (V_(1))/(V_(2))`
From (i) and (ii)
`" "_(3)n_(1)=" "_(3)n_(2) xx " "_(2)n_(1)`