Huygens' principle states that every point on a wavefront can be considered a source of secondary wavelets. The new wavefront is determined by the envelope of these secondary wavelets. Huygens used this principle to explain the laws of reflection and refraction. For refraction, the principle implies that the time taken for a wave to travel between two wavefronts is constant, regardless of the medium. This leads to Snell's law relating the sines of the angles of incidence and refraction to the ratio of velocities in each medium. For reflection, the principle shows that the angles of incidence and reflection are equal, in accordance with the first law of reflection.

1. Wave Optics : HUYGENS PRINCIPLE
A wave front is defined as a surface over which the phase of the wave is constant. In a
particular wave front, at a given moment of time, all particles of the medium are undergoing
the same motion.
WAVEFRONT

2. Wave Optics : HUYGENS PRINCIPLE

3. Wave Optics : HUYGENS PRINCIPLE

4. Wave Optics : HUYGENS PRINCIPLE

5. Wave Optics : HUYGENS PRINCIPLE

6. Wave Optics : HUYGENS PRINCIPLE
HUYGENS PRINCIPLE
Every particles of the medium situated on the wavefront act as a new
wave source from which fresh wave is originate .these waves are called
secondary wavelets.
The secondary wavelets travel in the medium in all directions with the
speed of the the original wave in the medium.
The envelope of the secondary wavelets in the forward direction at any
instant gives the
New wavefront at that instant.

7. Wave Optics : HUYGENS PRINCIPLE
Advantages:
Huygens concept proved the reflection and refraction of light.
The concepts like diffraction of light, as well as interference of light, were proved by Huygens.
Disadvantage:
Concepts like emission of light, absorption of light and polarisation of light were not explained by Huygens principle.
Huygens principle failed to explain the photoelectric effect.
A serious drawback is that the theory proposes an all-pervading medium required to propagate light called
luminiferous ether. This was proved to be false in the 20th century.

8. Wave Optics : HUYGENS PRINCIPLE
Huygens’ Principle and Laws of Refraction
The important considerations of Huygens’ Principle are:
All the rays, i.e., the tangents, are always perpendicular to the
primary wavefront.
The time taken by a wave to travel from one wavefront to
another will always remain constant. For a differing medium,
the density may cause a change in velocity and distance, but
time will remain the same.
All the points on a particular wavefront act like another source
of spherical waves called secondary wavelets

9. Wave Optics : HUYGENS PRINCIPLE
The velocity of light is changed when the light wave passes from one medium to another. This
phenomenon of the bending of light is called the refraction of light.
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

10. Wave Optics : HUYGENS PRINCIPLE
Considering the triangles ABC and ADC, we get:

11. Wave Optics : HUYGENS PRINCIPLE
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.

12. Wave Optics : HUYGENS PRINCIPLE
Proof of Refraction
Let the angle of incidence be i and the refraction is r.
From the ΔA1B’B1, we get
Sin∠B’A1B1 = Sin i = B’B/AB1
From the ΔA1CB1, we get
Sin∠A1B1C = Sin r = A1C/AB1
Sin i/Sin r = B’B/A1C
= v1t/v2t
Sin i/Sin r = v1/v2 = 1μ2(constant)
This proves Snell’s law of refraction. The constant 1μ2 is called
the refractive index of the second medium w.r.t the first
medium.

13. Wave Optics : HUYGENS PRINCIPLE
Huygens’ Principle and Laws of Reflection
If you look at the figure, AA’ is the wavefront incident on a
reflecting surface XY having an angle of incidence i. Following
Huygen’s principle, every point on AA’ will act as a source of
secondary wavelets.
Time taken from A’ to D = time taken from B’ to C
A’D / v = B’C / v
A’D = B’C
A’C sin(i) = A’C sin(r)
Thus, i = r
Hence, the angle of incidence and angle of reflection are both
equal. This is also stated by the first law of reflection.
Additionally, as the incident wavefront AB, the normal and
reflected wavefront are on the same plane, we can also verify
the second law of reflection.

14. Wave Optics : HUYGENS PRINCIPLE
The direction of propagation of the secondary wavelets is also the direction of propagation of their
primary wave sources.
It is also observed that the incident ray and the reflected ray lie on opposite sides of the normal.
The normal is perpendicular to the reflecting surface and originates at the point of incidence. The
normal, incident ray, and reflected ray lie on the same plane, and hence, the second law of
reflection is proven.

15. Wave Optics : HUYGENS PRINCIPLE