Hygens Principal Geometrical Path

Wave front: Locus of thr particle having same phase of medium in which a wave travel is called wavefront and a perpendicular drawn to wavefront away from source is called ray of light

Hygen’s Principal: Hygens’s principle states that
1. every point on the primary wavefront behaves as the source of secondary wavefront in all possible direction
2. The direction of secondary wavefront is given by the forward envelop on the primary wavefront
Diagram of a circle with small circle in its circumference
Let us consider s be the source of light which emit light waves in all possible direction. At time t light will move distance ct and forms a primary wavefront of radius ct. The point like a,b,c,d.... on primary wavefront are now the source of secondary wavefront and emit light in all possible direction. Again in further time delta t the source like a,b,c,d... forms the wave front of radius c delta t. The locus touching all the tangent points in forward direction in wavefront of source a,b,c,d... is the direction of secondary wavefront

Geometrical and optical path
The path travelled by the light in air or vaccum is called the optical path and the path travelled by light in certain medium is called geometrical path
Diagram with a arrow passing through a rectangle called medium
Let us consider light travel a distance x in certain medium maving refractive index meu in time t then
Geometrical path x = vt
where v = velocity of light in medium
t = x/v
Now we can have the optical path in same time
optical path = ct = c*x/v = c/v*x = meu *x = refractive index * geometrical path