Saved Bookmarks
| 1. |
How is a wavefront defined ? Using Hygen's construction draw a figure showing the propagation of a plane wave refracting at a plane surface separating two media. Hence verify Snell'a law of refraction. |
|
Answer» Solution :Wavefront : The continuous locus of all the particles of a medium, which are vibrating in the same phse is called a wavefront. (ii) Snell's law of refraction : Let `PP'` represent the SURFACE separating medium `1` andmedium `2` as shown in fig.  Let `v_(1)` and `v_(2)` represents the speed of light in medium `1` and medium `2` respectively. We assume a plane wavefront `AB` propagating in the direction `A'A` INCIDENT on the interface at an angle `i.` Let `t` be the time taken by the wavefront to travel the distance `BC`. `therefore BC=v_(1)t ["distance=speed"xx"time"],AE=v_(2)t` `therefore CE` would represent the refracted wavefront. In `Delta ABC` and `Delta AEC,` we have `sini =(BC)/(AC)=(v_(1)t)/(AC)` and `sinr=(AE)/(AC)=(v_(2)t)/(AC)` where `i` and `r` the angles of incident and refraction respectively. `therefore(sini)/(sinr)=(u_(1))/(AC).(AC)/(u_(2)t)` `(sini)/(sinr)=(u_(1))/(u_(2))` If `C` represents the speed of ligth in vacuum, then `n_(1)=(C)/(u_(1)) and n_(2)=(C)/(u_(2)) rArr v_(1)=(C)/(n_(1))and v_(2)(C)/(n_(2))` Where `n_(1) and n_(2)` are the refractive indices of medium `1` and medium `2`. `therefore (sini)/(sinr)=(C//n_(1))/(C//n_(2))rArr(sini)/(sinr)=(n_(2))/(n_(1))` `rArrn_(1)sini=n_(2)sinr` This is the Snell's law of refraction |
|