(i) Define refractive index of a medium.
(ii) In the following ray diagram, calculate the speed of light in the liquid of unknown refractive index.

Explanation

(i) It can be defined as the ratio of speed of light in vaccum or air to the speed of light in the medium.
It is denoted by `'n' = .^(c)//_(v)`
(ii) Here `tan .^(30)//_(40) = (3)/(4)`
So, `1 + tan^(2)c = 1 + (9)/(16) rArr sec^(2)c = (25)/(16) rArr 1 - cos^(2)c = 1 - (16)/(25)`
`rArr sin^(2) c = (9)/(25) rArr sin c = (3)/(5) = d (1)/(mu)`
so `mu = .^(5)//_(3)`
Also `mu = .^(5)//_(3) v = (c)/(mu) = (3 xx 10^(8))/(.^(5)//_(3)) = (9)/(5) xx 10^(8) = 1.8 xx 10^(8) m//s`