# Get the Knowledge that sets you free...Science and Math for K8 to K12 students

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## Interference and Diffraction

Fire rainbow and fiery moon The incredible, beautiful and rare lighting effect shown in the left part of the picture is formed as a result of sunlight passing through ice crystals in cirrus clouds covering the sky. The natural phenomena of light causing this effect, which is called 'rainbow film' or 'fire rainbow' is very rare to see, as the sunlight and ice crystals must be at a certain angle to each other. The right part of the picture shows the 'corona of moon' resulting from diffraction phenomena. The aureole is the first ring of the corona, consisting of a blue-white disk with the moon or sun at its center, bordered by a red-brown ring. Lets discuss more of such everyday aspects of light and its applications in this topic.

## After completing the topic, the student will be able to:

• Explore about the Huygens' principle of secondary wave fronts to analyze the phenomenon of reflection and refraction.
• Discover the phenomenon of interference using Young's double slit experiment.
• Illustrate and examine the Newton's rings and how they are used to characterize the lenses.
• Discuss and examine the phenomenon of diffraction to explore various observations in daily life.
• Observe and reflect on the phenomenon of dispersion and its relevance in everyday science.
• Discuss the concept of polarization and explore its applications in producing clean beams from a normal light.
• Examine and estimate selective absorption of different crystals based on the concept of polarization.
Rays and wave front Every point on the wave front acts as a source of secondary wavefronts.
Huygens' principle

Christiaan Huygens, a contemporary of Newton, is most remembered, for his idea about wave theory of light. He assumed that light wave is a transverse wave consisting of crests and troughs. Waves from a source of light propagate outwards. All points concentric to the source will have crests (or troughs) at the same distance. The curve where a disturbance is same is known as a wave front. For example, close to a light source, the wave fronts will be spherical; but if the light source is very far away, the wave fronts will be planar.

Huygens' principle states that every point on a propagating wave front serves as the source of spherical secondary wavelets, such that the wave front at some later time is the envelope of these wavelets. If the propagating wave has a frequency f, and is transmitted through the medium at a speed v, then the secondary wavelets will have the same frequency and speed. From this simple principle, Huygens was able to derive the laws of reflection and refraction.

Huygens' principle applied to a spherical wave front The direction of propagation of the wave is always perpendicular to the surface of the wavefront at each point. Thus, the wavefronts of a point source are spheres and the wave propagates radially outward.
Wave fronts

Although the wave fronts produced by a point source are always concentric spheres in principle, when the source is very far away the radii of the spheres are so large that they look like plane waves to an observer.

Consider the spherical wave front as shown in the adjacent figure. All points along the wave front AA' act as sources of new wavelets. After a short while the new overlapping wavelets will form a new surface, BB', which can be regarded as the envelope of all the wavelets.

Consider a plane wave front as shown in the next figure. In the figure we show only a few of the infinite number of wavelets from a few secondary point sources along AA' that combine to produce the smooth envelope BB'. As the wave spreads, a segment appears less curved. Very far from the original source, the waves nearly form a plane. E.g.: Waves from the sun.