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## Chapter: 12th Physics : UNIT 7 : Wave Optics

Physics : Wave Optics: Book Back Questions, Answers, Solutions: Short Answer Questions

1. What are the salient features of corpuscular theory of light?

1) According to Corpuscular theory, light is emitted as tiny, massless and perfectly elastic particles called corpuscles.

2) As the corpuscles are very small, the source of light does not suffer appreciable loss of mass even if it emits light for a long time.

3) On account of high speed, they are unaffected by the force of gravity and their path is a straight line in a medium of uniform refractive index.

4) The energy of light is the kinetic energy of these corpuscles.

5) When these corpuscles impinge on the retina of the eye, the vision is produced.

6) The different size of the corpuscles is the reason for different colours of light.

7) When the corpuscles approach a surface between two media, they are either attracted or repelled.

8) The reflection of light is due to the repulsion of the corpuscles by the medium and refraction of light is due to the attraction of the corpuscles by the medium.

2. What are the important points of wave theory of light?

According to wave theory, light is a disturbance from a source that travels as longitudinal mechanical waves through the ether medium that was presumed to pervade all space as mechanical wave requires medium for its propagation.

The wave theory could successfully explain the phenomena of reflection, refraction, interference and diffraction of light.

The existence of ether in all space was proved to be wrong. Hence this theory could not explain the propagation of light through vacuum.

The phenomenon of polarisation could not be explained by this theory.

3. What is the significance of electromagnetic wave theory of light?

Maxwell proved that light is an electromagnetic wave which is transverse in nature carrying electromagnetic energy. He could also show that no medium is necessary for the propagation of electromagnetic waves.

All the phenomenon of light could be successfully explained by this theory.

The interaction phenomenon of light with matter like photoelectric effect and Compton effect could not be explained by this theory.

4. Write a short note on quantum theory of light.

1) Albert Einstein was able to explain the photo electric effect in which photon interacts with matter to eject electrons on the basis of planck theory.

2) A photon is a discrete packet of energy, each photon has energy

E = hv

Where h = 6.625xl0-34 Js (planck's constant)

v = frequency of electromagnetic radiation.

3) As light has both wave as well as particle nature, it is said to have dual nature.

4) Thus light propagates as a wave and interacts with matter as a particle.

5. What is a wavefront?

A wavefront is the locus of points which are in the same state or phase of vibration.

When a wave propagates it is treated as the propagation of wavefront. The wavefront is always perpendicular to the direction of the propagation of the wave.

6. What are the shapes of wavefront for (a) source at infinite, (b) point source and (c) line source?

The shape of a wavefront observed at a point depends on the shape of the source and also the distance at which the source is located.

a) Any source that is located at infinity gives plane wavefront

b) A point source located at a finite distance gives spherical wavefronts.

c) An extended (or) line source at finite distance gives cylindrical wavefronts.

7. What is Huygens’ principle?

According to Huygens principle, each point on the wavefront behaves as the source of secondary wavelets spreading out in all directions with the speed of the wave. These are called as secondary wavelets.

The envelope to all these wavelets gives the position and shape of the new wavefront at a later time.

8. What is interference of light?

The phenomenon of superposition of two light waves which produces increase in intensity at some points and decrease in intensity at some other points is called interference of light.

9. What is phase of a wave?

Phase is the angular position of vibration when a wave is progresses, there is a relation between the phase of the vibration and the path travelled by the wave.

10. Obtain the relation between phase difference and path difference.

In the path of the wave, one wavelength λ corresponds to a phase of 2 π.

A path difference δ corresponds to a phase difference ϕ as given by the equation,

δ= [λ/2π] × Ø

or

Ø = [2π/ λ] × δ 11. What are coherent sources?

Two light sources are said to be coherent if they produce waves which have same phase or constant phase difference, same frequency or wavelength (monochromatic), same waveform and preferably same amplitude.

12. How does wavefront division provide coherent sources?

1) Wavefront division is the most commonly used method for producing two coherent sources.

2) We know a point source produces spherical wavefronts.

3) All the points on the wavefront are at the same phase.

4) If two points are chosen on the wavefront by using a double slit, the two points will act as coherent sources

13. What is intensity (or) amplitude division?

1) Intensity or amplitude division: If we allow light to pass through a partially silvered mirror, both reflection and refraction take place simultaneously.

2) As the two light beams are obtained from the same light source, the two divided light beams will be coherent beams.

3) They will be either in-phase or at constant phase difference.

4) Instruments like Michelson's interferometer, Fabry-Perot etalon work on this principle.

14. How do source and images behave as coherent sources?

1) A source and its image will act as a set of coherent source, because the source and its image will have waves in-phase or constant phase difference.

2) Fresnel's biprism uses two virtual sources as two coherent sources and Lloyd's mirror uses a source and its one virtual image as two coherent sources.

15. What is bandwidth of interference pattern?

The bandwidth (β) is defined as the distance between any two consecutive bright or dark fringes. β λD/d

16. What is diffraction?

Diffraction is bending of waves around sharp edges into the geometrically shadowed region.

17. Differentiate between Fresnel and Fraunhofer diffraction. Fresnel diffraction

i. Spherical or cylindrical wavefront undergoes diffraction

ii. Light wave is from a source at finite distance

iii. convex lenses need not be used in laboratory conditions

iv. Difficult to observe and analyse

Fraunhofer diffraction

i. Plane wavefront undergoes diffraction

ii. Light wave is from a source at infinity

iii. convex lenses are to be used in laboratory conditions

iv. Easy to observe, and analyse

18. Discuss the special cases on first minimum in Fraunhofer diffraction.

The equation for first minimum in single slit diffraction is, a sin θ = λ .

The angular spread for its first minimum in the diffraction pattern is

Sin θ = λ / a

The central maximum is found in between these first minima that occur on both the sides.

Special cases:

i) If a < λ , then sin θ > 1 which is not possible. Hence, diffraction does not take place.

ii) If a = λ , then sin θ =1 i.e. θ = 90°. The first minimum is at 90°. Hence, the central maximum spreads fully into the geometrically shadowed region leading to the bending of the diffracted light by 90°.

iii) If a > λ and also comparable to λ, say a = 2 λ, then sin θ = 1/2 (or) θ = 30°. The diffraction is observed with a measurable spread.

Hence, it is concluded that for observing the diffraction pattern, essentially the width of the slit 'a' must be just few times greater than the wavelength of light λ.

iv) If a >> λ, then sin θ < < 1 i.e. The first minimum falls within the width space of the slit itself. Hence, the phenomenon of diffraction is not observed at all.

19. What is Fresnel’s distance? Obtain the equation for Fresnel’s distance.

Fresnel's distance is the distance upto which ray optics is obeyed and beyond which ray optics is not obeyed but, wave optics becomes significant. From the diffraction equation for first minimum, sin θ = λ/a ; θ = λ/a

From the definition of Fresnel's distance, sin 2θ = a/z ; 2θ = a/z (or) θ = a/2z.

Equating the above two equation gives, λ/a = a/2z After rearranging, we get Fresnel's distance z as,

Z = a2 / 2λ

20. Mention the differences between interference and diffraction. Interference

•  Equally spaced bright and dark fringes

•  Equal intensity for all bright fringes

•  Large number of fringes are obtained

Diffraction

• Central bright is double the size of other fringes

• Intensity falls rapidly for higher order fringes

• Less number of fringes are obtained

21. What is a diffraction grating?

1) Grating has multiple slits with equal widths of comparable size to the wavelength of diffracting light.

2) Grating is a plane sheet of transparent material on which opaque rulings are made

3) A modern commercial grating contains about 6000 lines per centimetre.

22. What is resolution?

Resolution is measured by the smallest distance which could be seen clearly without the blur due to diffraction.

23. What is Rayleigh’s criterion?

According to Rayleigh's criterion, for two point objects to be just resolved, the minimum distance between their diffraction images must be in such a way that the central maximum of one coincides with the first minimum of the other and vice versa. The Rayleigh's criterion is said to be limit of resolution.

24. What is the difference between resolution and magnification? Resolution

• It is the ability of optical instruments to produce images that are clearer, finer, and sharper

• It allows us to see a object more clearly and with more details

• It can be expressed in arcsec or seconds

Magnification

• It is the ability of optical instruments to make a bigger image of an object

• It allows us to see small objects, especially those that are not visible to the naked eye

• It can be expressed by a whole number

25. What is polarisation?

The phenomenon of restricting the vibrations of light to a particular direction perpendicular to the direction of propagation of wave is called polarization of light.

26. Differentiate between polarised and unpolarised light Polarised Light

• Consists of waves having their electric and magnetic field vibrations in a single plane normal to the direction of ray.

• it is obtained from unpolarised light with the help of polarisers

Unpolarised Light

• Consists of waves having their electric and magnetic field vibrations in all directions normal to the direction of ray.

• Symmetrical about the ray direction

• Produced by conventional light sources.

27. Discuss polarisation by selective absorption.

1) Selective absorption is the property of a material which transmits waves whose electric field vibrations are in a plane parallel to a certain direction of orientation and absorbs all other vibrations.

2) The polaroids or polarisers are thin commercial sheets which make use of the property of selective absorption to produce plane polarised light.

3) Selective absorption is also called as dichroism.

28. What are polariser and analyser?

1) The Polaroid which polarises the light passing through it is called a polariser.

2) The polaroid which is used to examine whether a light is polarised or not is called an analyser.

29. What are plane polarised, unpolarised and partially polarised light?

1) A light is said to be plane polarized if the intensity varies from maximum to zero for every 90° rotation of the analyser.

2) If the intensity of light does not varies for rotation of the analyser then the light is said to be unpolarised light.

3) If the intensity of light varies between maximum and minimum (not zero) for every 90° rotation of the analyser, the light is said to be partially polarized light.

30. State and obtain Malus’ law.

E.N Malus discovered that when a beam of plane polarised light of intensity Io is incident on an analyser, the intensity of light I transmitted from the analyser varies directly as the square of the cosine of the angle θ between the transmission axes of polariser and analyser. This is known as Malus' law. Proof:

1) Consider the plane of polariser and analyser are inclined to each other at an angle θ is as shown in Figure.

2) Let Io be the intensity and  a  be the amplitude of the electric vector transmitted by the polariser.

3) The amplitude a of the incident light has two rectangular components, (acos θ) and (asin θ) which are the parallel and perpendicular components to the axis of transmission of the analyser.

4) Only the component acos θ will be transmitted by the analyser.

5) The intensity of light transmitted from the analyser is proportional to the square of the component of the amplitude transmitted by the analyser.

I (a cos θ)2

I = k (a cos θ)2

where k is constant of proportionality.

I = ka2cos2θ

I = Iocos2 θ

Where, I0 = ka2 is the maximum intensity of light transmitted through the analyser.

The following are few special cases.

Case (i) When θ = 0°, cos 0°= 1, I = Io

When the transmission axis of polariser is parallel to that of the analyser, the intensity of light transmitted from the analyser is equal to the incident light that falls on it from the polariser.

Case (ii) When θ = 90°, cos 90° = 0, I = 0

When the transmission axes of polariser and analyser are perpendicular to each other, the intensity of light transmitted from the analyser is zero.

31. List the uses of polaroids.

(i) Polaroids are used in goggles and cameras to avoid glare of light.

(ii) Polaroids are used to take 3D pictures i.e., in holography.

(iii) Polaroids are used to improve contrast in old oil paintings.

(iv) Polaroids are used in optical stress analysis.

(v) Polaroids are used as window glasses to control the intensity of incoming light.

(vi) Polarised laser beam acts as needle to read/write in compact discs (CDs).

(vii) Polarised light is used in liquid crystal display (LCD).

32. State Brewster’s law.

Brewster's law states that the tangent of the polarising angle for a transparent medium is equal to its refractive index.

tan ip = n

33. What is angle of polarisation and obtain the equation for angle of polarisation.

The angle of incidence for which the reflected light is found to be plane polarised is called polarizing angle or angle of polarization or Brewster's angle. It is denoted by ip.

According to Brewster's law

tan ip = n

ip = tan-1(n)

34. Discuss about pile of plates.

Pile of plates makes use of Brewster's law to convert the partially polarised refracted light into plane polarised light.

It consists of several plates kept one behind the other at an angle 90° − ip with the horizontal surface.

This arrangement ensures that the parallel light falls on these plates at ip.

When this unpolarised light passes successively through these plates, the few parallel vibrations to the surface which may be present in the refracted light, get a chance for further reflections at the succeeding plates.

Thus, both the reflected and the refracted lights are found to be plane polarised. 35. What is double refraction?

When a ray of unpolarised light is incident on a calcite crystal, two refracted rays are produced. Hence, two images of an object are formed. This phenomenon is called double refraction (or) birefringence.

36. Mention the types of optically active crystals with example.

Crystals like calcite, quartz, tourmaline and ice which have only one optic axis are called uniaxial crystals.

Crystals like mica, topaz, selenite and aragonite which have two optic axes are called biaxial crystals.

Principle:

The construction of a Nicol prism is based on the phenomenon of Double refraction.

Construction:

1) Nicol prism is calcite crystal which has a length three times is breadth and angles are 72o and 108o.

2) It is cut into two halves along the diagonal

3) The two halves are pasted together with a layer of canada balsam, a transparent coment. Working:

1) Consider a ray of unpolarised light from monochromatic source is incident on the Nicol prism.

2) Double refraction takes place and the ray is split into ordinary and extraordinary rays.

3) They travel in different directions with different velocities.

4) For monochromatic sodium light the refractive index of the crystal for the ordinary ray is 1.658 and for  extraordinary ray is 1.486. The refractive index of Canada balsam is 1.523.

5) The ordinary ray is total internally reflected at the layer of Canada balsam and is prevented from emerging along with extraordinary ray.

6) The extraordinary ray is transmitted through the crystal which is plane polarised.

38. How is polarisation of light obtained by scattering of light?

i) When sun light gets scattered by the atmospheric molecules, the electrons of these molecules are influenced by the vibrating components of the electric field present in the sun light.

ii) As the sunlight is unpolarised, it produces these vibrations in all directions.

iii) These vibrating electrons radiate energy only in the direction perpendicular to their vibrations.

iv) When an observer views a beam of sunlight perpendicular to its direction of travel, the radiations produced by the electrons vibrating in the direction perpendicular to the direction of view will only reach the observer.

v) Hence, the light reaching the observer is plane polarized. 39. What are near point and normal focusing?

Near point focusing:

The eye is least strained when image is formed at near point, ie. 25 cm

The near point is also called as least distance of distinct vision.

Normal focusing:

The eye is most relaxed when the image is formed at infinity. The focusing is called normal focusing when the image is formed at infinity.

40. Why is oil immersed objective preferred in a microscope?

In a microscope, smaller the value of dmin better will be the resolving power.

To reduce the value of dmin the optical path of the light is increased by immersing the objective of the microscope into a bath containing oil of refractive index n.

The value of dmin decreases by 1/n times. Hence, the resolving power is increases. Thus the oil immersed objective is preferred in a microscope to increase the resolving power of the microscope.

41. What are the advantages and disadvantages of using a reflecting telescope?

Only one surface it to be polished and maintained. Support can be given from the entire back of the mirror whereas it is given only at the rim for lens. Mirrors weigh much less compared to lens.

One obvious problem with a reflecting telescope is that the objective mirror would focus the light inside the telescope tube. One must have an eye piece inside obstructing some light.

42. What is the use of an erecting lens in a terrestrial telescope?

A terrestrial telescope is used to see object at long distance on the surface of earth. Hence, image should be erect.

Hence, it has an additional erecting lens to make the final image erect.

43. What is the use of collimator?

The collimator is used for producing a parallel beam of light.

44. What are the uses of spectrometer?

The spectrometer is an optical instrument used to analyze the spectra of different sources of light to measure the wavelength of different colours and to measure the refractive indices of materials of prisms.

45. What is myopia? What is its remedy?

A person suffering from nearsightedness or myopia cannot see distant objects clearly. This may be due to the short focal length of the eye lens (or) larger diameter of the eyeball than usual. This can be corrected using Concave Lens.

46. What is hypermetropia? What is its remedy?

A person suffering from farsightedness or hypermetropia or hyperopia cannot see closer object clearly. It occurs when the eye lens has long focal length or shortening of the eyeball than usual. It can be corrected using Convex Lens.

47. What is astigmatism? What is its remedy?

Astigmatism is the defect arising due to different curvatures along different planes in the eye lens. Astigmatic person cannot see in all the directions equally well. The defect due to astigmatism is more serious than myopia and hypermetropia. The remedy to astigmatism is using a lens which has different curvatures in different planes i.e. cyclindrical lenses.

48. What is presbyopia?

An aged people cannot strain their eye more to reduce the focal length of the eye lens. For clear vision, they should keep the object inconveniently away from their eye. Thus, reading or viewing smaller things held in the hand is difficult for them.

This kind of farsightedness arising due to aging is called Presbyopia.

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