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

Explanation

i. `""_(3)n_(1)` denotes refractive index of third medium with respect to first medium.
ii. Refractive index of third medium with respect to first medium is given by,
`""_(3)n_(1)=(v_(1))/(v_(3))`
Multiplying and dividing R.H.S. of above equation by `v_(2)`,
`""_(3)n_(1)=(v_(1))/(v_(2))xx(v_(2))/(v_(3))`
Since, `""_(2)n_(1)=(v_(1))/(v_(2)) and ""_(3)n_(2)=(v_(2))/(v_(3))`
`therefore" "_(3)n_(1)=""_(2)n_(1)xx""_(3)n_(2)`