##### Chapter 10

## Wave Optics

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

#### Introduction

**wave optics**posits that light travels as a wave. This means that it can bend around objects, diffract, and interfere. In the optical region, the wavelength of light is about half a micrometer.

In 1678, Dutch physicist, Christiaan Huygens had proposed the wave theory of light. This later became the cornerstone of **wave optics **and was used to derive laws of reflection and refraction.

According to this principle, every single point in a wave front can potentially produce secondary waves, and if you draw a tangent to all these spheres, it will give you the new position of the wave front at a later time.

If the shape of the waterfront at t=0, the **Huygens Wave Theory** will allow you to determine the shape of the waterfront at a later time τ.

Using an equation set, Maxwell had described the laws of electricity and magnetism and arrived at the famous wave equation. The latter was used to predict the existence of electromagnetic waves.

The wave equation gives the speed of electromagnetic waves in free space, that puts the theoretical value of the speed of light almost close to its measured value.

His theory posited that light is an electromagnetic wave, that changes with varying electric and magnetic fields. The latter leads to the emergence of electromagnetic waves, even in a vacuum.

A wavefront is defined as a surface of constant phase. A wavefront’s speed is measured by the speed at which it moves outward from the source. The wave energy travels in a perpendicular direction to the wavefront. Wave normal simply denotes a perpendicular drawn to the surface of waves.

In **wave optics, **there are two types of light sources:

1. Coherent sources emit light waves of the same wavelength and frequency. They have the same phase or a constant phase difference. To produce coherent waves, you can choose either of these two methods:

Division of Wavefront: The process of dividing the wavefront into two or more parts by using mirrors, lenses, or prisms.

Division of Amplitude: In this method, you can divide the amplitude of an incoming beam with the help of partial reflection or refraction.

2. Incoherent sources emit light waves that are characterized by frequent and random phase differences between photons. A popular example is the typical fluorescent tubes that you come across.

Wherever you witness two or more sources of light illuminating the same point, it means the **principle of superposition **is at play. This happens because there are interference terms, in addition to the sum of the individual intensities when you consider the intensity of light at the given point. Note that this occurrence is only true when the sources have the same frequency and stable phase difference, or a non-zero average.

In **plane polarized light, **the component electric field oscillates just like in ordinary light. The only and most significant difference, however, is that here the oscillation takes place in one single plane. The component magnetic field also oscillates within a single plane, and perpendicular to the electric field. In contrast, non-polarized light oscillates in multiple directions.

If you consider the vibration of a string in an x-z plane, generating a z-polarized wave, its displacement is given by,

z (x,t) = α sin (kx – ωt)

The study of **wave optics **is incomplete without understanding the basic **properties of waves. **There are four parts to waves:

**Frequency**

This is simply the number of waves passing through a point in a certain amount of time. Higher frequency is associated with greater energy produced by the waves since they are more tightly bound. Frequency is expressed by the formula,

f = 1/T, where f is the wave frequency in Hertz and T denotes the time period in seconds, or,

f = velocity/ wavelength = v/λ, where f is the wave frequency in Hertz, v is the velocity in metres/second, and λ denotes the wavelength.

**Amplitude**

The distance between a line through the middle of a wave and a crest or a trough. The highest point of a transverse wave is the crest, while its lowest point is the trough. Amplitude is expressed by the following equation,

y = Asin(ωt+φ), where y is the displacement of wave in meters, A denotes the amplitude, and ω is the angular frequency.

**Wavelength**

The distance between the crest of one wave and the crest of the very next wave gives you the wavelength. It is calculated as,

λ = velocity/ frequency = v/f, where λ denotes the wavelength, v is the velocity and f is the frequency of waves.

**Speed**

The distance travelled by a wave in a given amount of time is the speed of a wave. It is expressed with the following equation,

v = λf, where v is the velocity, λ is the wavelength and f is the frequency of the wave.

Wave Optics is a scoring topic in both boards as well as competition. You can check more about wave optics and more such topics with practical examples bringing the concept to life with videos on our MSVgo app.

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