# WAVE FRONT
It is the continuous locus of all the particle of a medium which
are vibrating in same phase.
Types of wave front:
1. Spherical wave front = When a source of light is points
source, the wave front is spherical wavefront.
2. Cylindrical wave front= When a source of light is linear is
called cylindrical wave front
3. Pane wave front= when point source and linear source are
at very large distance is called plane wave front.
# Huygen’s principle
According to Huygens principle,
It states that every point on a wavefront is a source of
spherical wavelets that spread out in all directions at the
speed of light. The sum of these wavelets forms a new
wavefront.
# proof of refection on the basis of wave theory
Laws of reflection
(i) Ist Law. It states that angle of incidence is equal to angle of
reflection.
(ii) 2nd Law. It states that the incident ray, the reflected ray and
the normal, at the point of incidence all lie in the same plane.
First law of reflection. Let XY be a plane reflecting surface and
AB be a plane wavefront incident on the surface as shown in the
figure.
According to Huygens principle, every point on wavefront AB is
a source of secondary wavelets and the time during which
wavelet from B reaches at C, the reflected wavelet from A would
arrive at D.
Laws of reflection
(i) Ist Law. It states that angle of incidence is equal to angle of
reflection.
(ii) 2nd Law. It states that the incident ray, the reflected ray and
the normal, at the point of incidence all lie in the same plane.
First law of reflection. Let XY be a plane reflecting surface and
AB be a plane wavefront incident on the surface as shown in the
figure.
According to Huygens. principle, every point on wavefront AB is
a source of secondary wavelets and the time during which
wavelet from B reaches at C, the reflected wavelet from A would
arrive at D.
i.e. t=BCv=ADv
or BC = AD, ...(i)
In rt ∠ΔABC ,
where v is the velocity of light in the medium.
sini=BCAC
In rt ∠ΔADC,sinr=ADAC
or BC=ACsini ...(ii)
or AD = AC sin r ...(iii)
Putting Eqs, (ii) and (iii) in (i), we get
AC sin i =AC sin r
or sin i = sin r
or i = r
i.e: Angle of incidence = angle of reflection
This is first law of reflection.
Second law of reflection. From the figure, we find that, the
incident ray, the reflected ray and the normal all lie on the same
plane XY. This proves second law of reflection.
# proof on refraction on the basis of wave theory
Let’s understand how Huygens’ Principle can help us prove the
laws of refraction with the help of the above diagram.
Considering a wavefront BC incident on the surface, we evaluate
that the incident ray has a velocity of V1 and the refracted ray
AD has a velocity of V2.
Since Huygens’ Principle states that despite differences in
density, the time taken by the waves to travel will be the same,
let’s assume the time taken is t.
Therefore, distance BC = V1t and AD = V2t.
Considering the triangles ABC and ADC, we get:
Here, μ is a constant. It represents the refractive index of the
medium through which the light rays are travelling. Another
keen observation is that the incident and refracted wavefront lie
on the same plane as the normal. This proves the 2nd law of
refraction.
The refractive index is also calculated as the ratio of the velocity
of light in a vacuum or air to the velocity of light in another
medium.
Hence, Snell’s law of refraction is proved via the application of
Huygens’ Principle. This proves the first law of refraction.
# Interference of waves
Wave interference is the phenomenon that occurs when two
waves meet while traveling along the same medium.
