Understanding Wave Phenomena: Huygens’ Principle, Reflection, Refraction, Polarization, Diffraction, and Interference
Block 5: Wave Phenomena
5.1. Huygens’ Principle
Waves exhibit unique qualities and phenomena not observed in other physical actions. These phenomena stem from the nature of wave propagation, which relies on the movement of successive wavefronts (a wavefront is a line connecting points with the same vibrational state). In the late 17th century, Dutch scientist Christiaan Huygens developed a geometrical method to predict the position of a wavefront at a specific time, given its previous position. This method, known as Huygens’ Principle, states that “every point on a wavefront acts as a source of new elementary waves (secondary waves) that propagate in the direction of the disturbance, and whose envelope forms the new wavefront.”
Consider a wavefront as depicted in the figure. Each point (a, b, c, d, etc.) acts as a source of secondary wavefronts. After a certain time, these partial waves will have traveled the same distance, reaching points a’, b’, c’, d’, etc. This formation of successive wavefronts illustrates the propagation of wave motion.
Huygens’ Principle elegantly explains various wave properties, including reflection, diffraction, refraction, polarization, and interference, by illustrating how wavefronts propagate and transmit energy.
5.2. Reflection
Reflection occurs when a wave changes direction upon encountering a surface separating two homogeneous and isotropic media.
Key elements involved in reflection include: the incident ray, the reflected ray, the normal (a line perpendicular to the surface at the point of incidence), the angle of incidence (angle i between the incident ray and the normal), and the angle of reflection (angle between the reflected ray and the normal).
Experimental observations have established the following laws of reflection:
- The incident ray, the normal, and the reflected ray lie in the same plane.
- The angle of incidence is equal to the angle of reflection.
5.3. Refraction
Refraction is the change in direction and speed of a wave as it passes from one medium to another with a different refractive index.
The elements involved in refraction are the incident ray, the refracted ray, the normal, the angle of incidence, and the angle of refraction.
Similar to reflection, the following laws of refraction have been experimentally verified:
- The incident ray, the normal, and the refracted ray lie in the same plane.
- The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in the two media:
– This is known as Snell’s Law of refraction.
When light passes from a medium with a lower refractive index (n1) to a medium with a higher refractive index (n2), such as from air to water, the refracted ray bends towards the normal. Conversely, when light travels from a higher to a lower refractive index, it bends away from the normal.
These laws can be explained using Huygens’ Principle.
5.4. Polarization
Longitudinal waves have only one direction of vibration. However, transverse waves can vibrate in infinitely many planes perpendicular to the direction of propagation. When a wave is restricted to vibrate in a single plane, it is said to be polarized. Polarization is a property exclusive to transverse waves.
The plane of polarization is defined by the direction of vibration and the direction of propagation. An example is a wave traveling along a string where all pulses are generated in the same plane.
5.5. Diffraction
Diffraction, derived from the Latin word diffractus meaning “broken,” describes the phenomenon of a wave bending around an obstacle or spreading out after passing through an opening. This deviation from straight-line propagation occurs when the size of the obstacle or opening is comparable to the wavelength of the wave. In essence, these points become sources of secondary waves, allowing the wave to reach areas not directly in the path of propagation.
Diffraction is fundamentally an interference phenomenon between two waves. It explains why we can hear a conversation from around a corner, even though we cannot see the speakers. The corner, with dimensions comparable to the wavelength of sound waves (2-3 meters), diffracts the sound waves. Light waves, however, are not diffracted as noticeably because their wavelengths are much smaller than the size of a typical corner or opening.
Diffraction also contributes to the reduced visibility in fog. Despite water being transparent, fog (composed of tiny water droplets suspended in the air) scatters light due to the droplets’ size being comparable to the wavelength of light. This scattering creates a seemingly opaque barrier, hindering visibility for drivers.
5.6. Interference and the Superposition Principle
Interference occurs when two or more waves traveling in different directions meet at a point. Experiments show that at the point of intersection, the waves combine their effects, and after passing through each other, they retain their original shape and energy. This ability of waves to intersect without altering their fundamental nature is a characteristic property of wave motion, distinguishing it from the collision of objects where original movements cease.
The outcome of interference is governed by the Superposition Principle: “When two or more waves converge at a point, the resulting disturbance at that point is the sum of the disturbances produced by each wave individually.”
When two waves of the same frequency from a coherent source intersect, the resulting motion can be amplified (constructive interference) or canceled out (destructive interference). In constructive interference, the resulting amplitude is greater than that of each individual wave, while in destructive interference, the resulting amplitude is smaller.
Constructive Interference vs. Destructive Interference
The types of waves that can interfere are diverse, and predicting the outcome can be complex. Let’s consider the simplest case: the interference of two coherent waves (vibrating in sync) with equal frequency, wavelength, and amplitude.
Suppose two waves interfere at point P, originating from sources O1 and O2 at distances x1 and x2 respectively. |
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The equations for these waves are:
y1(x1, t) = A sin(ωt – kx1)
y2(x2, t) = A sin(ωt – kx2)
Applying the Superposition Principle:
y = y1 + y2 = A[sin(ωt – kx1) + sin(ωt – kx2)]
Using the trigonometric identity:
We arrive at the expression:
