**Dual nature of Light and various Theories**

**Light** is a form of energy with the help of which we can see objects in our surroundings. The light exhibits **dual nature** i.e in some cases, **it behaves like a wave and particle respectively.** In case of ** Compton effect, Photoelectric and Pair production phenomenons,** the light behaves like a

**particle**while in case of

**the light behaves like a**

*Interference, Polarization, Reflection, Refraction, Diffraction,***wave.**Thus the light exhibits dual nature.

**History about the nature of Light**

As the light exhibits **dual nature,** during early times, this property of light made a great problem for the scientists to explain its real nature. The scientists gave their **ideas and theories** about light to support their conjectures.

**Newton’s Corpuscular Theory of Light**

The **corpuscular theory** of light was enunciated by** Newton.** It is also known as the particle theory of light. According to Newton, light travels from one place to another in the form of extremely small particles known as corpuscles. On the basis of this theory, Newton was able to explain the

*phenomenon of reflection and refraction of light.***Maxwell’s Theory of Light**

This theory was put forward by** Maxwell** in 1873. According to Maxwell, light is electromagnetic in nature, it consists of both

**electric vector ‘E’ and magnetic vector ‘H’,**both are oscillation perpendicularly to the direction of propagation of the waves. The speed of light is

**This thesis tells us that**

*3×10*^{8}m/sec.**light waves needs no material medium for their propagation.**Beside, it

**performed an experiment on the basis of which he explained the diffraction of light.**

*Thomas Young*In 1901, ** Planck** introduced

**‘Quantum theory’**of light. According to this thesis, light travels from one place to another in the form of discrete packets or bundles of energy which are known as

**‘Quantas’**or

**‘Photons’.**The energy of Photon is equal to

**The rest mass of photon is zero. The Quantum theory was able to explain the phenomenon of**

*‘hf’.*

*Photoelectric effect, Compton effect and Pair production.***Wave Theory of Light**

This theory was put forward by ** Huygen** which states that light travels from one place to another in the form of waves. This theory was able to explain

**reflection and refraction.**However, this theory was failed to explain the phenomenon of

*Polarization, Diffraction, and Interference of light.***Wavefront and its types**

** “The locus of all points in a medium with the same phase of vibration is known as wavefront”.** This could be easily explained from the fact that when we throw a piece of stone in to a pond of still water, then circular waves are produced. Now, the crest produced here is a wavefront because all the points on the crest will have

**same phase of vibration.**

**Types of Wavefront**

There are two types of wavefronts produced simultaneously in the path of wave motion on which the disturbances are in equal phase with each other. **Spherical and Plane wavefronts** in detail is mentioned below.

**Spherical Wavefront**

A wavefront which have concentric spheres with centres at its source is known as a spherical wavefront, as shown in the figure. In case of spherical wavefront, the energy of the wave is transmitted equally in all directions as the wave propagates. The direction in which the energy travel is known as the **‘Ray’.**

**Plane Wavefront**

At very large distance, **some portion of spherical wavefront appears a plane,** such straight portion of the wavefront is known as **plane wavefront. **The plane surfaces are parallel to each other. The rays are perpendicular to the plane surfaces.

**Huygen’s Principle**

According to **Huygen principle,** *“All points on a spherical wavefront acts as a point sources for the production of secondary spherical waves which are known as wavelets.”*

**Explanation**

Consider a source** ‘S’** which produces a wavefront

**as shown in the figure. Let us take several points in the form of dots on the wavefront**

*‘A’***These dots acts as secondary sources and each source produces spherical waves. Thus, using these points as secondary sources, we can easily draw spherical circles each having radius of**

*‘A’.***where**

*‘cΔt’,***‘c’**is the velocity of light and

**‘Δt’**represents the time interval during which a wave propagates from one wavefront to another. Consequently, the wavefront

**gives rise to another wavefront**

*‘A’***as depicted in the figure. Similarly, the wavefront**

*‘B’***will give rise to another wavefront**

*‘B’***and so on. This phenomena also occurs in the case of plane wave fronts, such principle is known as**

*‘C’*

*Huygen’s principle.***Coherent Sources**

Two sources of light are said to be coherent, if there is a **constant phase relationship** between the waves produced by them otherwise they are said to be incoherent sources.

**Production of Coherent Sources**

When light from a single source** ‘S’** is allowed to fall on a screen having two narrow openings, then the light which emerges out through the narrow openings becomes coherent. Thus, the openings or slits of the screen behaves as coherent sources of light.

**Examples of Coherent Sources**

The two vibrating spheres that produce water waves are **coherent sources** because the spheres vibrate up and down together.

The two slits in ** Young’s double slit experiment** are

**coherent sources**because the light from these sources originates from the same primary sources.

**Interference of Light**

*“The superposition of two coherent light waves traveling along the same medium in the same direction is known as interference of light”*

**Conditions for Interference**

**• The waves having same wavelength and time period should be emitted continuously from the two sources.**

**• The distance i.e path difference between the sources should be minimum.**

**• The amplitude of the two waves should be the same.**

**• Both the light sources should be narrow enough.**

**Types of Interference of Light**

There are two types of interference of light which are given below:

**Constructive interference**

** “Waves are said to interfere constructively when they reinforce the effect of each other simultaneously”**. Due to constructive interference, the resultant intensity of light increases and as a result bright fringes can be observed on the screen. For constructive interference, the crest of one wave should coincide with the crest of the another wave, while trough of one wave should coincide with the trough of the other wave.

**Destructive interference**

** “Waves are said to interfere destructively when they cancel the effect of each other simultaneously”.** Due to destructive interference, the resultant intensity of light decreases and as a result dark fringes are observed on the screen. For destructive interference, the amplitude of the resultant wave will be less than either of the individual waves. For destructive interference, the crest of one wave should coincide with the trough of the other wave.

**Condition for Constructive and Destructive interference**

For **constructive interference, **the ** path difference** between the two waves is an integral multiple of the wavelength i.e.

**p.d = mλ —> (1)**

where, ** m = 0,1,2,3**, etc. and

**λ = Wavelength of the coming from the source.**For destructive interference, the path difference between the two waves is an odd multiple of half of the wavelength i.e

**p.d = (m+1/2) λ —> (2)**

where, ** m = 0,1,2,3**, etc. and

**λ = wavelength of the coming from the source.****Young’s Double Slit Experiment**

Double slit experiment was devised by a **British polymath and physicist Thomas Young** in 1801 who made notable contributions to the fields of

**waves, light and vision, energy, solid mechanics, etc.**The main motive behind this famous experiment is to prove that light is a wave rather than a particle and study the interference of light but modern theories postulates that light exhibits dual behaviour of

**wave and particle respectively.**

**Experimental Arrangement**

The experimental setup consists of a light source ** ‘S’,** two slits

**and**

*‘S1’***and a screen as shown in the figure. A point**

*‘S2’,***on the screen is situated at a distance**

*‘P’***from the slit**

*‘r1’***and and at a distance**

*‘S1’***from the slit**

*‘r2’***respectively. While the separation between the two slits is represented by**

*‘S2’***There is another narrow slit**

*‘d’.***placed closer to the source of monochromatic light, as shown in the figure.**

*‘S*_{o}‘**Working**

Now, a beam of **monochromatic light** is allowed to pass through the narrow slit ** ‘S_{o}‘** and then through

**and**

*‘S1’***The waves passes through**

*‘S2’.***‘S1’**and

**‘S2’**produces interferences of light at point

**‘ on the screen as shown in the figure.**

*‘P***Path Difference**

From the figure, we see that** r2>r1.** The distance difference between them us known as path difference. To find the ** path difference,** we draw perpendicular line from

*on*

**‘S1’***as shown in the figure. Now, in*

**‘r2’****△S1DS2,**we have:

**sinθ = △r/d ⟹ △r = dsinθ —> (1)**

Equation **(1)** represents the** path difference.** Now, there will be

**constructive interference,**if:

**△r = dsinθ = mλ —> (2) **

where **m = 0,1,2,3, etc.** and **λ = Wavelength of the light**

Now, there will be **destructive interference,** if:

**△r = dsinθ = (m+1/2)λ —> (3)**

**Position of Bright and Dark Fringes on the Screen**

In order to find out the **position** of **bright **or **dark fringes** on the screen, we use the triangle **“△ROP”,** in which **tanθ = y _{m}/L ⟹ y_{m} = Ltanθ —> (4)**

Now, if* L>>d *and point

**is very close to point**

*‘p’***then we put**

*‘O’,***tanθ = sinθ.**Thus equation

**(4)**becomes

**y _{m} = Lsinθ —> (5)**

Now, for **constructive interference,** we have:

**dsinθ = mλ ⟹ sinθ = mλ/d —> (6)**

Putting equation **(6)** in equation **(5),** we get:

*y _{m} = Lmλ/d —> (7)*

**Equation (7) represents the position of mth bright fringes on the screen.**

Now, for **destructive interference,** we have:

**dsinθ = (m+1/2)λ ⟹ sinθ = (m+1/2)λ/d —> (8)**

Putting equation **(8)** in equation **(5),** we get:

*y _{m} = L(m+1/2)λ/d —> (9)*

**Equation (9) represents the position of mth dark fringes on the screen.**

**Fringe Width**

** “The distance between two consecutive dark or bright fringes is known as fringe width or fringe spacing”.** Now for finding the fringe spacing, we use different method for dark and bright fringes respectively.

**Dark Fringes**

We subtract the first order dark fringe from the second order dark fringe i.e, we have:

**Fringe space _{dark}**

**= y**

_{2}-y_{1}**⟹ Fringe space _{dark}**

**= 5Lλ/2d – 3Lλ/2d**

**⟹ Fringe space _{dark}**

**=**

*Lλ/d*

*—> (10)***Bright Fringes**

We subtract the first order bright fringe from the second order bright fringe i.e, we have:

**Fringe space _{bright}**

**= y**

_{2}– y_{1}**⟹ Fringe space _{bright} = 5Lλ/d – Lλ/d**

**⟹ Fringe space _{bright}**

**= Lλ/d**

*—> (11)***Uses of Young’s Double Slits Experiment**

**• It gives us the experimental verification of wave theory of light.**

**• It can be used to study the phenomenon of interference.**

**• It is used for the determination of fringe width.**

**• It can be used for finding the wavelength of light.**

**Diffraction of Light**

*“The spreading of light waves around the edges of a narrow opening is known as diffraction”.*

OR

*“The spreading of light into the region behind an obstacle is known as diffraction”.*

OR

*“The deviation of light from its original path is known as diffraction”.*

**Explanation**

Consider a wedge placed in the path of a beam of light coming from its source ** ‘S’** as shown in the figure. When the beam of light strike the wedge, it deviate from its path through an angle

**as shown in the figure. As a result, the original position**

*θ*_{1},θ_{2},θ_{3}, etc.**on the screen will appear dark and we will observe the diffraction fringes at the points**

*‘O’***and**

*‘A’***above the central point**

*‘B’***Such deviation of light from its original path is known as diffraction of light.**

*‘O’.***Fraunhofer Diffraction due to a Single Slit**

Consider a beam of monochromatic light of wavelength** ‘λ’** falls on a slit Ab having width

**as shown in the figure. In order to observe the diffraction pattern, a screen**

*‘d’***is placed parallel to the slit**

*‘S’***The rays i.e. wavelets are focused on the screen with the help of a convex lens. A small portion of the incident wavefront pass through the narrow slit. Each point of this section of the wavefront sends out secondary wavelets to the screen.**

*‘AB’.*The wavelets interfere to produce the diffraction pattern on the screen. Now, let the waves** ‘1’ and ‘5’ **are in phase. When these waves reach the wavefront ‘

**wave**

*AC’,***would have a**

*‘5’***path difference**If

*‘ab’.***ab = λ/2,**then the two rays will reach the point

**on the screen resulting in destructive interference. Similarly, each pair**

*‘P’***and**

*‘2’*

*‘6’, ‘3’*and*‘7’, ‘4’***and**differ in path by

*‘8’,***Hence, they will also interfere destructively.**

*‘λ/2’.*Now, to find the value of **path difference ‘ab’,** we use the triangle

**in which we have:**

*△abA,**sinθ = ab / (AB/2)*

*ab = (AB/2) sinθ*

**ab = (d/2) sinθ —> (1)****∵** **AB = d**

For **destructive interference, **we have:

*ab = λ / 2*

From equation **(1),** we have:

**⟹** **λ /2 = (d/2) sinθ**

*d sinθ = λ —> (2)*

Equation **(2)** represents the **first order minimum (dark).** In general, equation **(2)** can be written as:

** d sinθ = mλ —> (3),** where

**m = 1,2,3, etc.**

The region between any** two consecutive minima **will be **maxima (bright).** Thus, a series of **bright and dark (maxima and minima) regions are observed on the screen.** The first bright region is situated at the centre of the pattern, as shown in the figure.