Define term, "refreactive index " of a medium. Verify Snell's law refraction when a plane wavefront is propagating from a denser to a rarer medium.

Explanation

Refrative Index : Refractive Index is the ratio of the sine of angle of incidence to the sine of the angle of refraction.

`1mu_(2)` is the refractive index of 2nd medium w.r.t. Ist medum.
Laws of refraction of the basis of Huygen's wave theory : Let PP' represents the medium (1) and medium (II). Let `v_(1)" and "v_(2)` represent the speed of light in medium (I) and medium (II) respectively. Let AB be the incident wave front and EC be the refracted wave front.

`BC==v_(1)t," "AE=v_(2)t`
`"In "DeltaABC, sini=(BC)/(AC)=(v_(1)t)/(AC)" ....(1)"`
`"In "DeltaCAE, sin r=(AE)/(AC)=(v_(2)t)/(AC)" ....(2)"`
Dividing equation no. (1) and (2)
`(sini)/(sinr)=(v_(1)t)/(AC)xx(AC)/(v_(2)t)=v_(1)/v_(2)="constant"`
Let C be the speed of light
`mu_(1)=c/v_(1)" rArr "v_(1)=c/mu_(1)" ...(3)"`
`mu_(2)=c/v_(2)" rArr "v_(2)=c/mu_(2)" ...(4)"`
Dividing equation (3) and (4)
`v_(1)/v_(2)=mu_(2)/mu_(1)=(sini)/(sinr)`
`mu_(2)sinr=mu_(1)sini.` This proves the Snell's law of refraction.