Introduction

Wave optics is the branch of physics that deals with propagation, production and emission of light and study various phenomenon like interference, diffraction and polarization of light.

Optics

It is a branch of physics that deals with the study of optical phenomenon like reflection, refraction, dispersion, interference, diffraction, etc.

Furthermore, this branch is divided into two parts:

1. Ray optics
2. Wave or physical optics

Wave Optics

It is defined as the branch of optics that deals with the production, emission and propagation of light, its nature and the study of the phenomenon like interference, diffraction and polarization.

In the early times, scientists have made a discussion on the nature and propagation of light and proposed various theories. Some of them are as follows:

i. Newton’s Corpuscular Theory

According to this theory, Newton in 1678 proposed that light consists of very tiny particles called corpuscles. These particles are tiny, massless, elastic and travels in a straight line. They travel with speed of 3 x 10⁸ ms^-1. This theory successfully explained:

1. Rectilinear propagation of light
2. Reflection of light as the corpuscles bounce back when it strikes the reflecting surface.
3. Refraction of light because these corpuscles when travels from rarer to denser medium the particles in the denser medium pulls the particles with greater force. And they bend towards the normal.

This theory failed because:

1. It claimed that the velocity of light in denser medium is greater than rarer medium.
2. It could not explain the phenomenon of light like interference, diffraction, polarization, etc.

ii. Huygen’s Wave Theory

In 1690, a Dutch scientist Christian Huygen proposed a new theory of light on the basis of wave nature. According to this theory, light propagates from the source in the form of a wave where a medium is required for propagation. For the propagation in space, it was assumed that there is a highly dense, elastic medium called ether medium. This theory successful explained:

1. Reflection of light
2. Refraction of light
3. Interference & diffraction of light

But this theory could not explain the polarization nature of light as it can be proved with light’s transverse nature, which was proved by a scientist Fresnel.

iii. Electromagnetic Theory

It was proposed by Maxwell in 1860. According to this theory, light is a electromagnetic wave and it gets propagated in the form of electric and magnetic field vibrating perpendicularly with the direction of propagation of wave.

iv. Quantum Theory

It was proposed by Einstein in 1905. According to this theory, light is transmitted as tiny packets of energy called photon.

v. Dual Nature of Light

From the discussions with various theories, it was found that light possesses dual nature i.e., waves as well as particle nature.

Wavefront: (Single circle = 1 wavefront)

Wavefront is the locus of all vibrating particles which are in same phase. The shape of wavefronts is different according to the nature and distance from the source of light. Every point on the wavefront acts as a source of disturbance, these disturbances from the points are called wavelets.

Types of wavefront

a) Spherical wavefront

They are formed by point source of light, because all such points are equidistant from the source, lie on a sphere.

b) Cylindrical wavefront

They are formed by a linear source of light, because all points are equidistant from the source, lie on a cylinder.

c) Plane wavefront

A small portion of cylindrical or spherical wavefront originating from a distant source will appear as a plane and they are called plane wavefront.

Electromagnetic Spectrum

The orderly distribution of electromagnetic radiations according to their wavelength or frequency is called electromagnetic spectrum.

The classifications of the electromagnetic spectrum are explained as:

(i) Radio waves

Range: frequency: few Hz to 10⁹ Hz

Uses:

• Radio & TV broadcasting system, oscillating circuits having inductor and capacitor.

(ii) Microwaves

Range: wavelength: 1 mm to 30 cm. (frequency: 10⁹ Hz to 3 x 10¹¹ Hz).

Uses:

• Radar communication
• Aircraft navigation
• Microwave ovens for cooking purpose

(iii) Infrared (IR) rays

Range: wavelength: 700 nm to 1 mm (frequency: 3 x 10¹¹ Hz to 4.3 x 10¹⁴ Hz)

Uses:

• Night vision glasses
• They are used to keep the green houses warm.
• To treat muscular strains.

(iv) Visible Light

Range: wavelength: 400 nm to 700 nm (frequency: 4.3 x 10¹⁴ Hz to 7.5 x 10¹⁴ Hz)

Uses:

• It stimulates the sense of sight to see the world.
• Used for photography.
• Used in optical microscopy.

(v) Ultraviolet Rays (UV rays)

Range: wavelength: 60 nm to 400 nm (frequency: 7.5 x 10¹⁴ Hz to 5 x 10¹⁵ Hz)

Uses:

• Used to kill bacteria and germs in the drinking water.
• Used to sterilize the surgical instruments.
• To study the structure of molecules.

(vi) X-rays

Range: wavelength: 60 nm to 10^-8 nm (frequency: 5 x 10¹⁵ Hz to 3 x 10¹⁸ Hz)

Uses:

• Used in medical diagnosis like locating the fracture in bone.
• Used in radio therapy to cure skin diseases, cancers, etc.
• Used by detective agencies to detect gold, silver and other foreign elements in the bags or body.

(vii) Gamma rays

Range: wavelength: 0.1 nm to 10^-5 nm (frequency: 3 x 10¹⁸ Hz to 3 x 10²² Hz)

Uses:

• Used to treat cancer.
• To examine the thick materials for structural flaws.

Huygen’s principal

Huygen’s principal is geometrical construction of a wavefront which is used to determine the position of wavefront at a later time from its position at any instant. This principle is based on the following assumptions:

1. Each point on the primary (given) wavefront acts as a source of secondary wavelets, the light waves sending out from secondary sources travel in all direction with speed of light.
2. The new position of the wavefront at any instant is given by the forward envelope of the secondary wavelets at that instant.

To illustrate it, let AE be a portion of primary wavefront, at an instant. To find position of secondary wavefront after time t, let, five points A, B, C, D, E on primary wavefront AE. Light travels ‘ct’ distance in time ‘t’, ‘c’ being speed of light. Taking each point as centre, draw a sphere of radius = ct. This spherical surface represents secondary wavefront. There are forward as well as backward wavefront, but backward secondary wavefront is contrary to observation. So, there is no backward flow of energy during propagation of wave.

Laws of reflection on the basis of wave theory

To prove laws of reflection, let us take a plane wavefront AE incident on reflecting surface XY, as shown in figure alongside. By the time (t), the disturbance from point E reaches at point C, at the same time, secondary wavelet travels from A reach to B and covers a distance of ct.

From A, draw a sphere having radius AB and from E having radius EC, which represent the secondary wavelet. The forward tangent of which, represents the reflected wavefront.

Draw NA and N’C in normal to XY. Then,

∠EAC = angle of incidence (i) and

∠BCA = angle of reflection (r)

In fig

EC = AB= ct

In triangle AEC

Sini = EC/AC

Sini = ct/AC ………………… (i)

Similarly in triangle ABC

Sinr = AB/AC

Sinr = ct/AC …………….. (ii)

From equations (i) and (ii),

Sini= Sinr

i.e., ∠i = ∠r, which is first law of reflection. From figure, incident wavefront, normal and reflected wavefront all lie in the same plane. This proves the second law of reflection.

Laws of refraction on the basis of wave theory

Consider, a plane wavefront AB incident on a boundary PQ separating media (1) and (2). Let, v₁ and v₂ be the velocity of incident wave and reflected wave (v₁ > v₂). The first point on the boundary to be hit by incident wave front at A and last is C. From Huygen’s principal, every point, between A and C in turn, becomes a source of secondary spherical wavelets. Let ‘t’ be time taken by disturbance at B to reach C.

∴ BC = v₁t …….  (1)

During this time, the secondary wavelet created at A has travelled a distance AD = v₂t in the medium (ii) with A as centre and AD as radius draw a circle. This circle represents secondary spherical wave front at time ‘t’, that had emerged from A, t second earlier. Thus, envelope to wavelets is refracted wavefront CFD.

In [latex]\Delta ABC, Sini = \frac{BC}{AC}[/latex]

In [latex]\Delta ACD, Sinr = \frac{AD}{AC}[/latex]

∴ [latex]\frac{Sini}{Sinr} = \frac{BC}{AC}\times \frac{AC}{AD} = \frac{BC}{AD}[/latex]

Or, [latex]\frac{Sini}{Sinr} = \frac{v_1 t}{v_2 t} \frac{v_1}{v_2}[/latex]

∴ [latex]\frac{Sini}{Sinr} = \mu_2^1[/latex], is refractive index of medium (2) w.r.t medium (1), which is Snell’s law. Hence, laws of refraction are explained on the basis of wave theory.