Proof of Reflection

Huygens was the one who contradicted Newton’s theory of light having a particle nature. He proposed that light has wave properties. The contradiction concluded by stating that light has both particle and wave nature. Huygens and Fresnel, together, put forth a principle describing the movement and formation of wavelets from the previously formed ones.

Huygen’s principle of secondary wavelets also paved the way to analyse and determine the position of a wavelet from the known position of the previous one. The Huygens-Fresnel principle applies to all types of waves, including light, sound, and water. Huygen’s principle works out for the proof of reflection. Proof of reflection is given below.

Huygens-Fresnel principle

• Christiaan Huygens and Augustin-Jean Fresnel proposed their theory in the year 1690.

• The Huygens-Fresnel principle of secondary wavelets states that the wavelets originate from every possible wavefront point of its precursor wave. 

• The wavelet originates and travels forward along the tangent drawn to the wavefront point.

• The point at the wavefront is the source of the birth of the secondary wavelets.

• It is applied in problems like wave propagation and the position of the secondary wavelet.

• The time taken for the formation of the secondary wavelet from the primary one is constant, but the waves settle with time.

Wavefront

• Wavefront is the point or locus where the waves are at the same phase.

• There are three different types of wavefronts.

Spherical wavefront – the waves are circular and concentric.

Planar wavefront – the waves seen are only a small part of the spherical wave and are linear.

Cylindrical wavefront – the wave is cylindrical, having equal distances from the centre to the horizon of the wave. It forms when the waves pass through a narrow slit.

Reflection 

• When the waves that hit a plane mirror transmit back, it is called reflection.

• According to Snell’s law, the angle of incidence is the same as the angle of reflection.

∠i = ∠r

• Reflection refers to switching the direction of waves due to interference or an obstacle by another medium. 

Types of reflection

Based on the direction and the angle of the reflected rays, the type of reflection varies.

Specular reflection 

The light falls on the plane mirror surface and reflects at the same angle. It is called specular reflection.

Diffuse reflection 

The light falls on the plane mirror and bounces back at different angles. It is called diffuse reflection.

Retro reflection 

When the incident light ray reflects along the same path of its incidence, it is retroreflection.

Multiple reflections 

When several mirrors are placed along the path of reflection of the initial incident ray, the rays are reflected continuously and form multiple reflections, as well as multiple images.

Proof of reflection

The Huygens principle declared the proof of reflection, refraction, and diffraction of light. As per the proof of reflection notes, let’s understand the Huygens principle – 

Consider the light rays’ A’ and ‘B’ falling on the plane mirror at a point of incidence A’ and B’.

They get reflected at an angle of ‘i’ and ‘r’, respectively, as the reflected rays’ P’ and ‘Q’.  

sin(i) =  sin(r)

Thus, i = r.

It proves both the first and second law of reflection.

The first law of reflection

According to the first law of reflection, the angle of incidence(i) and the angle of reflection(r) are equal when the light rays incident on a plane mirror.

The second law of reflection

As per the second law of reflection, the ray of incidence, the Normal line at the point of incidence, and the ray of reflection lie on the same plane.

The third law of reflection

Per the third law of reflection, the ray of incidence(i) and the ray of reflection(r) lie on opposite sides of the Normal line of the mirror.

Reflection of waves

The reflection of waves can be observed in certain real-life situations on our planet.

• Reflection of waves due to collision with each other is evident when we hear echoes in an empty place.

• The principle of reflection of waves is used in sonar detectors.

• It is crucial in detecting and monitoring the seismic activity of the earth.

• The waves of the surface of the water bodies exhibit reflection of water waves.

• It is apparent in certain electromagnetic waves.

• It is helpful for radio transmission rays and radars.

• It is used in constructing instruments that analyse the structure of a substance.

Conclusion

The proof of reflection is evident by Huygens principle. All three laws of reflection are proved by Huygens principle. Proof of reflection notes provides three laws of reflection: (i)the incident angle is equal to the reflected angle; (ii) the incident ray, the reflected ray and the normal of the incident point lie in the same plane; (iii) the incident ray lies opposite to the reflected rays. 

Huygen and Fresnel proposed that the secondary wavelets originate from the previously formed primary wavefronts. Any point on the wavefront is the source of origin of a new secondary wavelet. Huygen’s principle also satisfies laws of refraction and diffraction.