Reflection laws proof using Huygen's principle | Wave optics | Physics | Khan Academy

Summary

The video explains Huygens' principle, which describes light as a wave and how wavefronts evolve. It demonstrates how each point on a wavefront becomes a source of secondary waves, with their common tangent forming a new wavefront. Using this principle, the video proves the law of reflection, showing that the angle of incidence equals the angle of reflection. It includes a step-by-step geometric construction, using rays and wavefronts, and highlights the symmetry in the process. Finally, the video hints at refraction, where wave speeds differ, making the angles unequal.

Takeaways

• 🌊 Huygens' principle states that every point on a wavefront acts as a source of secondary waves.
• 🔄 The envelope of these secondary waves, specifically their common tangent, forms the new wavefront.
• 🪞 To demonstrate reflection, a mirror is used where each point acts as a source of reflected waves.
• 📏 When drawing reflected wavefronts, only one circle from each Huygens source is needed to determine the tangent.
• 🕒 The radius of the secondary waves should be equal to the distance the incident wavefront traveled to ensure accurate reflection.
• 📐 The reflected wavefront is perpendicular to the incident ray, maintaining the property of wavefronts.
• 📏 To prove the law of reflection (angle of incidence equals angle of reflection), rays are drawn parallel to the wavefront.
• 📐 A normal is dropped at the point of incidence to define the angles of incidence (i) and reflection (r).
• 🔍 By examining the geometry of the situation, two right-angle triangles are identified, which are key to proving the law.
• 📐 Using the RHS (Right Angle-Hypotenuse-Side) postulate, the congruence of the triangles is established, proving i = r.
• 🔄 The speed equality of the incident and reflected waves is crucial for the angles to be equal, a concept that differs in refraction.

Q & A

What is Huygens' principle?

Huygens' principle states that every point on a wavefront acts as a source of secondary spherical wavelets, and the new wavefront is the common tangent to these wavelets. This principle can be used to describe the evolution of wavefronts, such as light waves.

How does Huygens' principle help explain the laws of reflection?

Huygens' principle shows that each point on an incident wavefront hitting a mirror becomes a source for secondary waves. The reflected wavefront is formed by drawing a common tangent to these secondary waves, demonstrating that the angle of incidence equals the angle of reflection.

What is a wavefront and how is it represented in this explanation?

A wavefront can be thought of as a set of oscillating particles moving in sync. In this explanation, wavefronts are represented as lines perpendicular to the incident rays of light, showing the progression of light waves.

How do you determine the size of the secondary wavelets in the reflected wavefront?

The radius of the secondary wavelets is equal to the distance traveled by the incident wave in the same amount of time, as both the incident and reflected waves travel at the same speed.

Why do we only need one circle to draw the reflected wavefront?

When drawing the reflected wavefront, only one secondary wavelet from the mirror is needed to determine the tangent, which represents the reflected wavefront. The other wavelets aren't necessary for this construction.

What role does geometry play in proving the law of reflection?

Geometry helps prove that the angle of incidence equals the angle of reflection by comparing the congruent triangles formed by the incident and reflected rays. The sides and angles of these triangles are shown to be equal.

How do you construct the incident and reflected rays using wavefronts?

The incident rays are drawn first, and the wavefront is drawn perpendicular to them. For the reflected wavefront, you draw a tangent to the secondary wavelet, and then the reflected rays are drawn perpendicular to the reflected wavefront.

Why is it important that the reflected wave travels at the same speed as the incident wave?

The fact that the reflected wave travels at the same speed as the incident wave allows the radii of the secondary wavelets to be equal to the distance traveled by the incident wave. This ensures that the reflected wavefront can be accurately constructed.

How does Huygens' principle differ in explaining refraction versus reflection?

In reflection, the speed of the wave remains the same, so the angles of incidence and reflection are equal. However, in refraction, the wave changes speed as it moves between different media, leading to different angles of incidence and refraction.

What is the significance of the tangent in Huygens' principle?

The tangent in Huygens' principle represents the new wavefront. For reflection, the common tangent to the secondary waves gives the reflected wavefront, showing how the wave progresses after hitting a reflective surface.