Wave Optics - Class 12 Physics Chapter 10

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Wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid.

Huygens Principle

Huygens principle is one of the key methods for studying various optical phenomena. The principle is a method of analysis applied to problems of wave propagation both in the far-field limit and in near-field diffraction and also reflection. It states that “Every point on a wavefront is in itself the source of spherical wavelets which spread out in the forward direction at the speed of light. The sum of these spherical wavelets forms the wavefront”.

Huygens Principle, also known as the Huygens–Fresnel principle highlights the following wave propagation behaviour:

  • Secondary sources form their own wavelets that are similar to the of the primary source.
  • At any given point in time, the common tangent on the wavelets in the forward direction gives the new wavefront.
  • The wavefront is the sum of the spherical wavelets.

Refraction and Reflection of plane waves using Huygens Principle

Refraction is the bending of waves when passes through a different medium.

Reflection is the process in which light waves falls on a surface and bounces back.

In refraction, the sine of angle between the incident ray and normal maintains a constant ratio with the sine of angle of refracted ray and normal. Snell’s Law of refraction is proved using Huygens’s principle

The incident ray, the refracted ray and the normal to the refracting surface lie in the same plane.

The laws of reflections are verified using Huygens’s Principle. The incident ray, the reflected ray and normal to the reflecting surface lie in one plane which is perpendicular to the reflecting surface. The angle of incidence equals angle of reflection.

Coherent and incoherent addition of waves

Interference is a natural phenomenon that happens at every place and at every moment. The most commonly seen interference is the optical interference or light interference. This is because light waves are randomly generated every which way by most sources. This means that light waves coming out of a source do not have a constant amplitude, frequency or phase.

Interference of light waves and young’s experiment

Interference of Light Waves is defined as the modification in the distribution of light energy when two or more waves superimpose each other. For Interference the waves emitted by sources should be with zero phase difference or no phase difference. These sources should emit continuous waves of same wave length and same time period.

Thomas young performed the famous interference experiment which is the Ydse. It was by this experiment; the wave theory of light came into existence. In this experiment, Thomas Young used one single light source and it was the passed through two slits to obtain two coherent sources. Thus each slit act as a light source.

Diffraction

Diffraction is the slight bending of light as it passes around the edge of an object. The amount of bending depends on the relative size of the wavelength of light to the size of the opening. If the opening is much larger than the light's wavelength, the bending will be almost unnoticeable.

The single slit

In the single-slit diffraction experiment, we can observe the bending phenomenon of light or diffraction that causes light from a coherent source interfere with itself and produce a distinctive pattern on the screen called the diffraction pattern. Diffraction is evident when the sources are small enough that they are relatively the size of the wavelength of light.

Seeing the single slit diffraction pattern

In interference and diffraction, light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe. There is no gain or loss of energy, which is consistent with the principle of conservation of energy.

Resolving power of optical instruments

Resolving power is defined as the inverse of the distance between two objects which can be just resolved when viewed through the optical instrument. Optical instruments should be able to display two separate images as distinct two separate images.

Suppose if we are seeing 2 stars in the sky using telescope, and they are very closely placed to each other, they should not be displaced as one star. Instead they should be displaced as two separate stars. The ability to see them as separate 2 stars is known as resolving power.

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