Optics subjective question 1

Question
A narrow monochromatic beam of light of intensity I is incident on a glass plate A as shown below in the figure

Another identical glass plate B is kept close to A  and parallel to it. Each glass plate reflects 25% of the light intensity incident on it and transmits the remaining.Find the ratio of maximum and minimum intensities in the interference pattern formed by the two beams obtained after reflection from each plate.

Solution:

Hi First try to solve the question on your own it's an easy one . The answer is ratio of intensities is 49. I will provide the solution to this question.

For solution visit link

polarisation and polarised light

Light wave is said to be polarised when the vibration of its electric vector are confined to one direction in plane perpandicular to its direction of propagation.

When light is polarised its intensity reduces to 50% of the intensity of unpolarised lighy.

when we pass a polarised light through a polaroid and we rotate the polaroid about the direction of propagation of the light then the intensity of light changes as per the Law of Malus where intensity I=I₀cos²θ

Polarised light can be obtained by reflection , refraction and scattering of unpolarised light.

Polarisation of light can only be detected by a polaroid.

What is diffraction

It is a common observation with the waves of all kinds that they bend round the edge of an obstacle.

Light like other waves also bends round the corner but in comparison to sound waves small bending of light is due to very short wavelength of light which is of the order of 10^-5 cm.

This effect of bending of light beams round the corner was first discovered by Grimaldi (1618-1663).

We now define diffraction of light as phenomenon of bending of light waves around the corners and their spreading into geometrical shadow.

Fresnel first explained that the diffraction phenomenon was the result of mutual interference between the secondary wavelets from the same wavefront.

Thus we can explain diffraction phenomenon using Huygen's principle.

The diffraction phenomenon is usually divided into two classes
1. Fresnel class of diffraction phenomenon where the source of light and scteen are in general at finite distance from the diffracting aperture
2. Fraunhofer class of diffraction phenomenon where source and the screen are at the infinite distance from the aperture , this is easily achieved by placing the source of light on the focal plane of a convex lens and placing screen on focal plane of another convex lens. This class of diffraction is simple to treat and easy to observe in practice.

Coherent Sources of light

Coherent sources are those sources of light which emit continous light waves of same wavelength , same frequency and are in same phase or have constant phase difference.

For observing interference phenomenon coherence of light waves is a must.

For light waves emitted by two sources of light , to remain coherent the initial phase difference between waves should remain constant in time. If the phase difference changes continously or randomly with time then the sources are incoherent.

Two independent sources of light are not coherent and hence can not produce interference because light beam is emitted by millions of atoms radiating independently so the phase difference between waves from such sources fluctuates randomly many times per second.

The coherent sources can be obtained either by the source and obtaining its virtual image or by obtaining two virtual images of the same source. This is because any change of phase in real source will cause a simultaneous and equal change in its image.

Generally coherence in interference is obtained by two methods
(1) Division of wave front where wavefront is divided into two parts by reflection, refraction or diffraction and those two parts reunite at a small angle to produce interference as done in case of Young's double slit experiment and Fresnel's biprism experiment.
(2) Division of amplitude where amplitude of a section of wavefront is divided into two parts and reunited later to produce interference such as in case of thin films.

Laser light is almost monochromatic light with little spreading and two independent sources of laser light can produce observable interference pattern.

Light : Waves or particles

When we think of light a question comes to our mind whether it light is a wave or a particle. This discussion is very interesting and has got a long history. Newton the great physicist tried to understand travel of light in straight line assuming that a luminous body emits very minute and weightless particles called corpuscles travelling through empty space in straight line in all directions with the speed of light and carry kinetic energy with them. Thus energy is carried by stream of particles travelling with a finite velocity , this is the basic principle behind what we call the Corpuscular theory proposed by Sir Issac Newton.  This Corpuscular theory of light can fairly explain the phenomenon of reflection , refraction and rectilinear propagation of light but failed to explain phenomenon of interference , diffraction and polarization of light.
           A new theory of propagation of light was suggested by Dutch physicist Christian Huygens in 1678 in which he suggested that light may be a wave phenomenon produced by mechanical vibrations of an all pervading hypothetical homogeneous medium called ether just like those in liquids and solid. This medium was supposed to be mass less with extremely high elasticity and very low density. In this theory there is a transfer of energy by wave motion without actual travelling of matter. At first wave theory of light was not accepted primarily because of Newton's authority and also because light could travel through vacuum and waves require a medium to propagate from one place to another. Wave theory of light first begin to gain acceptance when double slit experiment of Thomas Young in 1801 firmly established that light is indeed a wave phenomenon. After this double slit interference experiment many experiments were carried out by scientists involving interference and diffraction of light which could only be explained by assuming wave model of light.
          Later on in nineteenth century Maxwell put forward his electromagnetic theory and predicted the existence of electromagnetic waves and calculated the speed of EM waves in free space and fount that this value was very close to the measured value of speed of light in vacuum. He then suggested that light must be an EM wave associated with changing electric and magnetic fields which results the propagation of light or EM waves even in the vacuum. So this way mo material medium is required for the propagation of light wave travelling from one place to another. This fact established that light is a wave phenomenon.
           But this is not the end of the story Hertz first observed the phenomenon of photoelectric effect in1800 according to which when light falls on metal surface , electrons are emitted from the metal surface and the kinetic energy of the electrons does not depend on the intensity of light used. This phenomenon was latter explained successfully by another great physicist Albert Einstein in 1905 by assuming light as photons the quanta of light. His theory again gave rise to the old discussion whether light is a wave or particle. Later on well established particles like electrons also shows diffraction phenomenon under suitable conditions and such effects csn be studied under wave particle duality beyond the scope of this article. 

Wave Optics : Part 2

• In Young’s Experiment two parallel and very close slits S1and S2 (illuminated by other another narrow slit) behaves like two coherent sources and produces a pattern of dark and bright bands (interference fringes) on a screen. For a point P on the screen
  
  S2P-S1P≈y1d/D1
  
  Where d is the separation distance between two slits, D1 is the distance between the slits and the screen and y1 is the distance of point P from the central fringe.
  
  
• For constructive interference (bright band) , the path difference must be an integral multiple of wavelength λ i.e.,
  
  y1d/D1 = n λ or y1=nD1λ/d
  
  
• The separation distance Δy1 between adjacent bright or dark fringes is
  
  Δy1 = D1λ/d
  
  Using this relation we can calculate wavelength λ.
  
  
• The colors shown by thin films are due to interference between two beams , one reflected from the top surface of the film and other from the bottom. The path difference between the two may give constructive interference for one color and destructive interference for another. Hence the reflected light is colored.
  
  
• Term diffraction refers to light spreading out from narrow holes and slits, and bending around corners and obstacles.
  
  
• The single slit diffraction pattern shows the central maximum (θ=0) at angular separation θ=±n λ (n≠0) and secondary maxima at θ=±(n+1/2) λ (n≠0).
  
  
• Different parts of the wave front at the slit acts as secondary sources ; diffraction pattern is the result of interference of waves from these sources.
  
  
• An aperture of size a sends diffracted light into an angle ≈ λ/a.
  
  
• Doppler effect is the shift in frequency of light when there is a relative motion between the source and the observer. It is given by
  
  Δν/ν ≈ vr/c for v/c << 1
  
  Where vr is the radial component of relative velocity v. This effect can be used to measure the speed of an approaching or receding object.
  
  
• Polarization specifies the manner in which electric field E oscillates in the plane transverse to direction of propagation of light. If E oscillates back and forth in a straight line , the wave is said to be linearly polarized. If the direction of E changes irregularly then the wave is un-polarized.
  
  

Wave Optics : Part 1

1. A wavefront is the locus of points having same phase of oscillation.
2. Rays are lines perpandicular to the wavefront, which shows the direction of propagation of energy.
3. The time taken for light to travel from one wavefront to another is same along any ray.
4. Huygen's construction is based on the principle that every point of a wavefront is the source of secondary wavefront that is the surface tangent to all secondary wavefronts gives rise to a new wavefront.
5. The law of refraction (i=r) and the Snell's law of refraction
sini /sinr =v₁/v₂=n₂/n₁ = n₂₁
can be derived using the wave theory. Here v₁ and v₂ are the speed of light in media 1 and 2 wiyh refractive index n₁ and n₂ respectively.
6. The frequency ν remains same when light travels from one medium to another. The speed of the wave is given by
v=λ/T=λν
where λ is the wavelength of the wave and T is the period of oscillation.
7. Emission , absorption and scattering are the three proscesses by which matter interacts with radiation.
8. In emission , an accelerated charge radiates an looses energy.
9. In absorption the charge gains energy at the expence of the EM wave.
10. In scattering the charge accelerated by incident EM wave radiated in all direction.
11. Two sources of light are coherent if they have same frequency and stable phase difference.
12. In case of coherent sources of light the total intensity I  is not just the sum of individual intensities I₁ and I₂ due to two sources but also includes an interference term that is
I = I₁ + I₂ + 2kE₁.E₂
where E₁ and E₂ are the electric fields at a point due to the sources.
13. The interference term averaged over many cycles is zero if (i) the source of light have different frequencies or (ii) the source have the same frequency but not stable phase difference. For such incoherent sources I = I₁ + I₂