"Light + Light" need not always give more light, but may in certain circumstances give 'darkness'. - Max Born

       Light when passed through a pinhole it will have particle nature. The same light when passed through two pinholes of same nature adjacent to each other it will have wave nature. Does it mean the Light knows whether it is passing through a single pinhole or two holes even before it passes through them? Does it mean that Light possesses consciousness?
 

Interference of Light
Young Double slit experiment:
        Light passing through a pinhole passes through an arrangement of two pinholes similar in all respects kept at certain distance from the source when caught on a screen the Light on the screen instead of having same intensity, form dark and bright bands. Here the light from one hole is interfering with that of the other and the phenomenon is called 'Interference'. This crucial experiment was done by Thomas Young.

Young's Double Slit Experiment 

*   The phenomenon of Interference could not be explained by Newton's Corpuscular theory.
*   The property of interference can be exhibited only by 'Waves'. So, Christian Huygens confirmed that Light propagates only as a wave and proposed 'Wave theory of Light'.

*   Interference of Light waves is the modification of Light intensity due to the superposition of two or more coherent Light waves.
*   Two waves are said to be 'coherent' if they are in phase with each other or have a phase difference that remains constant with time.
      Let the amplitude of each wave is 'a' and 'δ' be the phase difference between them by the time t, they reach the screen.
*   If y₁, y₂ are the displacements of the waves after a time t then y₁ = a sin ωt and
      y₂ = a sin (ωt + δ) where ω is the angular frequency of the waves.
*   If these two waves superimpose interfere the resultant amplitude.
       y = y₁ + y₂ = a sin ωt + a sin (ωt + δ)
*   It can be proved y = R sin (ωt + δ) where R is the amplitude due to interference.

*   Since the intensity of light (I) is equal to the square of the amplitude 

Special cases
1.   If δ = 0, 2Π, 2(2Π), .... n(2Π)
       Intensity of light I = 4 a² [cos²( 0/2 )] = 4 a²
       Intensity of Light will be maximum. Bright bands will form.
2.   If δ = Π, 3Π, 5Π ....., (2n + 1)Π
       Intensity of light I = 4 a² [cos² Π/2 ] = 0
       Intensity of light will be zero and dark bands will form
*   Band width where D is the distance between the coherent sources (slits) and the screen
λ - wave length of light               d - distance between the slits.
Applications
1. The wavelength of monochromatic light can be determined.
2. The difference in wavelength between two closely placed spectral lines can be found.
3. The refractive indices of liquids and gases can be determined accurately.
4. Whether the outer surfaces of objects are perfectly smooth and plane can be determined.

5. The refractivity of prisms and lenses can be found.
6. Thickness of transparent substances like thin glass plates can be determined. Just before sunrise, if the mountains in east obstruct the sun, and we can observe at the edges of the mountains a bright silvery glow.
 

Diffraction of Light

Will light rays bend? 
*   Just before sunrise, if the mountains in east obstruct the sun, and we can observe at the edges of the mountains a bright silvery glow.
*   If the fingers of a hand are kept closely and observe a far off light source through the narrow gaps between the fingers, we can observe thin lines of light in the forms of bands.
*   If light rays are passed through a pinhole or a narrow slit or a sharp edge like a razor blade, in the dark zones of their shadows dark and bright fringes can be seen.
*   It means whenever light is made to pass at the edges of sharp objects, it will bend and spreads through certain extent in their shadows. This spreading or bending of light around the edges of obstacles is called the phenomenon of 'Diffraction'.
*   Diffraction can be explained only by a wave theory. Diffraction occurs as a result of the superposition of secondary wavelets from a continuous section of a wave front that has been limited by an aperture or opaque obstacle.

Condition for diffraction of Light
   The condition for observing diffraction of light waves by an obstacle or an aperture or a slit is 

     Where 'L' is the distance between the obstacle and the screen where the diffraction effects can be observed , λ is the wavelength of light and 'b' is the size of the obstacle.
Explanation: Hyugens-Fresnel Principle

      Let us consider a wavefront S. P is the point at which the resultant amplitude due to the wavefront is to be found. 'dS' is the area of an element of the wave front.
→ According to Huygens- Fresnel Principle.
→ Diffraction occurs when a wavefront is partially obstructed.
→ All the points in an obstructed portion of the wavefront act like secondary sources.
→ The secondary waves from these sources are coherent.
→ The amplitude 'dA' at P due to the element 'dS' depends on the distance 'r' and the angle  θ (called obliquity) between the normal 'n' to the wavefront and the line that joins 'dS' and P.
→ The resultant amplitude 'A' at 'P' due to the whole wave front is obtained by integrating over the entire wavefront 'S'.
A = ∫ dA
    Diffraction is studied under two classes
1. Fresnel Diffraction       2. Fraunhofer Diffraction.

Fresnel Diffraction:
       Here, the source and the screen are at finite distances from the diffracting aperture or obstacle.Hence the wavefronts that fall on the diffracting aperture and those that leave it and proceed to the screen are not plane. No lenses are required to observe Fresnel Diffraction. The light rays are not parallel.
Fraunhofer Diffraction:
       Here, both the source and the screen are at infinite distances from the diffracting aperture or obstacle. Hence, the incident and the diffracted wavefronts are plane wavefronts. This can be realised by using convex lenses one on either side of the diffracting aperture or obstacle.
General Conditions:
    Let 'L' be the distance between the screen and the obstacle, 'b' is the size of the obstacle and 'λ' is the wavelength of the light.
*   if   < < 1, Fraunhofer diffraction can be observed
*   if    = 1, Fresnel diffraction can be observed

 

Applications of diffraction
*   Diffraction gratings (multiple slits) are used to determine the wavelength of light.
*   X - ray diffraction methods are used to find the wavelength of X - rays.
*   The structure of crystals are determined by diffraction techniques involving X - rays, electrons and neutrons.
*   In medical diagnosis, diffraction of ultrasonic waves is used to determine the size and shape of ulcers and tumours.
*   Diffraction of ultrasonic waves is used to find the velocity of sound waves in organic and inorganic liquids.
Polarization
Waves are of two types. 1. Longitudinal waves   2. Transverse waves.
Interference and diffraction established that light is a wave but these phenomenon have not shown which type of waves are light waves.

Earlier, Huygens assumed the light waves are longitudinal nature, but the phenomenon of 'Polarization' exhibited by light later, established that it is a transverse wave. This fact is established by the following experiment.
Experiment

In this experiment light from a source (S) is made to incident on tourmaline crystal T₁ which is cut parallel to its principal axis. Now light passes through the crystal and falls on the screen with certain intensity. Now even if S is rotated in its place there will not be any change in the intensity of light emerging out of the crystal. Now if another tourmaline crystal T₂ similar to T₁ placed parallel to T₁. Certain facts will be revealed if the following observations are made
*   If both crystals are rotated at a time through equal extent, both their axes will be parallel to each other. There will not be any change in the intensity of emerging light.
*   If T₁ is kept vertically and without moving it if T₂ is rotated, the intensity of emerging light will gradually decrease. If T₁ and T₂ are mutually perpendicular no light is emitted i.e., intensity of light will be zero. If T₂ is further rotated, light emerges from it once again and it reaches its maximum intensity when T₁ and T₂ are parallel to each other.
*   This experiment confirms that light wave is a 'Transverse wave'.
*   Light rays emerging from the source of light will be vibrating randomly in all directions.
     The above experiment shows that Light waves after passing through T₁ are travelling in a single direction which means the other components are completely destroyed.

*   The light wave having vibrations in all directions after passing through tourmaline crystal having vibration only in a single direction is called 'Polarization'. Polarization occurs because of vibrations in a single direction.
*   The plane in which light vibrations are absent is called 'polarising plane'.
*   The plane where light vibrations occur is called 'vibrating plane'.
*   Plane polarization can be produced by i) reflection ii) refraction and iii) double refraction.
 

Double refraction
      A Scientist by name Enasmus-Bartholinus observed two refracted rays instead of one when light is passed through a calcite crystal.
*   If an ink mark is made on a paper over which a calcite crystal is kept and observed vertically, two refracted images of the ink mark are seen. Now if the crystal is rotated slowly in its place, one of the images will be stationary which is called 'Ordinary image' and the second image rotates along with the crystal. This is called 'extra ordinary image'.
*   The light rays associated with ordinary image obey 'Laws of refraction'. Refractive index remains constant.
*   The light rays associated with extraordinary image will not obey 'Laws of refraction'.

The value of refractive index will not be constant and it will be changing with angle of incidence..
 

Polariods
→ The polarizing materials which are made artificially are called 'Polaroids'This is a commercial name.
→ Polaroid's are used to produce 'Polarization of light' and also to analyse Polarized light.
→ Polaroid's are used in 3D-Cinemas, Polarized Spectacles. These eye glasses will decrease the intensity of sun light and protect the eyes.
→ Polarized light is used to measure optical rotation in Glucose solution, and to study helical structure in nucleic acids.
→ Polarized light is used to find structure of atoms, their size and shape in matter.