Saved Bookmarks
| 1. |
Define wavefront of a travelling wave. Using Huygens principle, obtain the law of refraction at a plane interface when light passes from rarer to a denser medium. |
|
Answer» Solution :A wavefront is a surface of constant phase. CONSIDER a plane surface XY separating a rarer medium of refractive index `n_(1)` from a denser medium of refractive index `n_(2)`. Let `c_(1) and c_2` be the values of speed of light in the two media. AB is a plane wavefront incident on XY at an angle i. Let at a given INSTANT the end of wavefront just strikes the surface XY but the other end B has still to cover a path BC. If it takes time t, then `BC= c_(1)t.` According to Huygen.s principle, point A meanwhile begins to emit secondary wavelength which will cover a distance `c_(2)t` in second medium in time t. Draw a circular arc with A as centre and `c_(2)t` at as radius and draw a tangent CD from point C on this arc. Then CD is the refracted wavefront, which subtends an angle r from surface XY.  Now in `TRIANGLEABC SIN i=(BC)/(AC)=(c_(1)t)/(AC)` and in `triangleADC sin r=(AD)/(AC)=(c_(2)t)/(AC)` `(sin i)/(sin r)=(c_(1) t//AC)/(c_(2)t//AC)=c_(1)/c_(2)="a constant" =(n_(2))/(n_(1))=n_(21)` Which is Snell.s law of refraction. |
|