Wave Optics

Question 1

Who proposed the corpuscular model of light in 1637, and what did it predict about the speed of light in different mediums?

Answer 1

The corpuscular model of light was proposed by Descartes in 1637. It predicted that if a ray of light bends towards the normal upon refraction, then the speed of light would be greater in the second medium.

Question 2

Who further developed the corpuscular model of light in his book OPTICKS, and why is the corpuscular model often attributed to him?

Answer 2

Isaac Newton further developed the corpuscular model of light in his book OPTICKS. It is often attributed to him due to the tremendous popularity of his book.

Question 3

What theory of light did Christiaan Huygens propose in 1678, and what phenomena could it satisfactorily explain?

Answer 3

Christiaan Huygens proposed the wave theory of light in 1678. It could satisfactorily explain the phenomena of reflection and refraction.

Question 4

What contradiction did the wave theory of light pose regarding the speed of light in different mediums upon refraction, and when was this contradiction confirmed by experiments?

Answer 4

The wave theory predicted that if a wave bends towards the normal upon refraction, then the speed of light would be less in the second medium, contrary to the corpuscular model. This contradiction was confirmed by experiments in 1850 by Foucault, showing that the speed of light in water is less than in air.

Question 5

Why was the wave theory of light not readily accepted initially, and what experiment by Thomas Young firmly established it?

Answer 5

The wave theory of light was not readily accepted initially due to Newton’s authority and the belief that light required a medium for propagation. Thomas Young’s interference experiment in 1801 firmly established the wave nature of light.

Question 6

What is the field of optics called when the finiteness of the wavelength is neglected, and what is a ray defined as in this field?

Answer 6

The field of optics when the finiteness of the wavelength is neglected is called geometrical optics. A ray is defined as the path of energy propagation in the limit of wavelength tending to zero.

Question 7

How did Maxwell explain the propagation of light waves through vacuum, and what did he derive from his equations?

Answer 7

Maxwell explained the propagation of light waves through vacuum by proposing his electromagnetic theory of light. From his equations, Maxwell derived the wave equation and predicted the existence of electromagnetic waves. He found that the theoretical speed of these waves in free space closely matched the measured speed of light.

Question 8

What principle will be discussed first in this chapter, and what laws will be derived from it?

Answer 8

The original formulation of the Huygens principle will be discussed first in this chapter. Laws of reflection and refraction will be derived from it.

Question 9

What phenomenon will be discussed in Sections 10.4 and 10.5, and what principle is it based on?

Answer 9

Interference will be discussed in Sections 10.4 and 10.5, based on the principle of superposition.

Question 10

What phenomenon will be discussed in Section 10.6, and what principle is it based on?

Answer 10

Diffraction will be discussed in Section 10.6, based on the Huygens-Fresnel principle.

Question 11

What is a wavefront and how is it defined?

Answer 11

A wavefront is a surface of constant phase. It is defined as the locus of points where the disturbance of a wave is maximum and all points on the surface oscillate in phase due to being at the same distance from the source.

Question 12

How does a point source emitting waves uniformly in all directions create wavefronts?

Answer 12

A point source emitting waves uniformly in all directions creates spherical wavefronts. These wavefronts consist of spheres where all points have the same amplitude and vibrate in the same phase.

Question 13

What happens to a spherical wavefront at a large distance from the source?

Answer 13

At a large distance from the source, a small portion of the spherical wavefront appears as a plane. This configuration is known as a plane wave.

Question 14

Explain Huygens principle and its application in determining wavefront shapes.

Answer 14

Huygens principle allows us to determine the shape of wavefronts at a later time by considering each point on the wavefront as the source of secondary wavelets. These secondary wavelets spread out in all directions with the speed of the wave. By drawing spheres centered at each point on the initial wavefront and finding their common tangent, we can determine the shape of the wavefront at a later time.

Question 15

What is the shortcoming of Huygens’ model in determining wavefront shapes?

Answer 15

The shortcoming of Huygens’ model is the presence of a backwave, which contradicts observations. Huygens proposed an ad hoc assumption that the amplitude of secondary wavelets is maximum in the forward direction and zero in the backward direction to explain the absence of the backwave.

Question 16

How can Huygens principle be applied to determine the shape of wavefronts for a plane wave propagating through a medium?

Answer 16

Huygens principle can be applied to determine the shape of wavefronts for a plane wave by considering each point on the wavefront as the source of secondary wavelets. Drawing spheres centered at each point and finding their common tangent allows us to determine the shape of the wavefront at a later time.

Question 17

What does PP¢ represent in the context of deriving the laws of refraction?

Answer 17

PP¢ represents the surface separating medium 1 and medium 2.

Question 18

What do v1 and v2 represent in the context of deriving the laws of refraction?

Answer 18

v1 represents the speed of light in medium 1, and v2 represents the speed of light in medium 2.

Question 19

Define the angle of incidence and angle of refraction.

Answer 19

The angle of incidence, denoted by i, is the angle between the incident ray and the normal to the surface, while the angle of refraction, denoted by r, is the angle between the refracted ray and the normal to the surface.

Question 20

What is Snell’s law of refraction?

Answer 20

Snell’s law of refraction states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media.

Question 21

What is the critical angle?

Answer 21

The critical angle, denoted by i_c, is the angle of incidence at which the angle of refraction becomes 90 degrees, resulting in total internal reflection.

Question 22

Describe the law of reflection.

Answer 22

The law of reflection states that the angle of incidence is equal to the angle of reflection, where both angles are measured with respect to the normal to the surface.

Question 23

How does a convex lens affect a plane wave passing through it?

Answer 23

A convex lens causes the lower portion of the incoming wavefront to be delayed, resulting in a tilt in the emerging wavefront.

Question 24

What happens to a plane wave incident on a thin convex lens?

Answer 24

The central part of the incident plane wave traverses the thickest portion of the lens and is delayed the most, resulting in a depression at the centre of the emerging wavefront, which becomes spherical and converges to the focal point.

Question 25

Explain the principle behind the behavior of light passing through a convex mirror.

Answer 25

Light incident on a convex mirror results in a spherical wave converging to the focal point, similar to the behavior observed in concave mirrors.

Question 26

What principle ensures that the total time taken from a point on the object to the corresponding point on the image is the same along any ray?

Answer 26

The principle of equal time along any ray ensures that the total time taken from a point on the object to the corresponding point on the image remains constant, regardless of the path taken by the light rays.

Question 27

Who was Christiaan Huygens?

Answer 27

Christiaan Huygens was a Dutch physicist, astronomer, mathematician, and the founder of the wave theory of light.

Question 28

What is notable about Huygens’ book “Treatise on Light”?

Answer 28

Huygens’ “Treatise on Light” is notable for its fascinating content, even by today’s standards. It brilliantly explains phenomena such as double refraction, reflection, and refraction.

Question 29

What significant discovery did Huygens make about the mineral calcite?

Answer 29

Huygens explained the double refraction exhibited by the mineral calcite in his work.

Question 30

Aside from his work on light, what other scientific contributions did Huygens make?

Answer 30

Huygens was the first to analyze circular and simple harmonic motion. Additionally, he designed and built improved clocks and telescopes.

Question 31

What did Huygens discover about Saturn’s rings?

Answer 31

Huygens discovered the true geometry of Saturn’s rings.

Question 32

What principle is the entire field of interference based on?

Answer 32

The entire field of interference is based on the superposition principle, which states that at a particular point in the medium, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each of the waves.

Question 33

How do two sources become coherent in interference?

Answer 33

Two sources become coherent when the phase difference between the displacements produced by each of the waves does not change with time.

Question 34

How are constructive interference and destructive interference defined?

Answer 34

Constructive interference occurs when two waves interfere in such a way that their displacements add up, resulting in an increase in intensity. Destructive interference occurs when two waves interfere in such a way that their displacements cancel each other out, resulting in a decrease in intensity or complete cancellation.

Question 35

What condition leads to constructive interference?

Answer 35

Constructive interference occurs at an arbitrary point P when the path difference, S1P ~ S2P, equals nl (where n is any integer including zero).

Question 36

What condition leads to destructive interference?

Answer 36

Destructive interference occurs at an arbitrary point P when the path difference, S1P ~ S2P, equals (n+1/2)l (where n is any integer).

Question 37

What is the intensity at a point in interference if the phase difference between the two displacements is zero or a multiple of 2π?

Answer 37

When the phase difference is zero or a multiple of 2π, constructive interference occurs, leading to maximum intensity, which is four times the intensity produced by each individual source.

Question 38

What is the intensity at a point in interference if the phase difference between the two displacements is π or an odd multiple of π?

Answer 38

When the phase difference is π or an odd multiple of π, destructive interference occurs, leading to zero intensity.

Question 39

What is the resultant displacement and intensity at an arbitrary point G in interference?

Answer 39

At an arbitrary point G, the resultant displacement is given by y = 2a cos (f/2) cos (wt + f/2), and the intensity is given by I = 4I0 cos^2(f/2), where f is the phase difference between the two displacements.

Question 40

How does coherence affect the stability of interference patterns?

Answer 40

If two sources are coherent, maintaining a constant phase difference, the interference pattern will be stable over time. However, if the phase difference changes rapidly with time, the interference pattern will also change rapidly, resulting in a time-averaged intensity distribution.

Question 41

What happens to interference patterns when two sources are incoherent?

Answer 41

When two sources are incoherent, the interference patterns change rapidly with time, resulting in a time-averaged intensity distribution where the intensities just add up.

Question 42

Why do we not observe any interference fringes when using two sodium lamps illuminating two pinholes?

Answer 42

We do not observe interference fringes because the light waves emitted from ordinary sources undergo abrupt phase changes in times of the order of 10–10 seconds, resulting in incoherent light waves from independent sources.

Question 43

How did Thomas Young lock the phases of waves emanating from S1 and S2?

Answer 43

Thomas Young achieved phase locking by creating two pinholes (S1 and S2) close to each other on an opaque screen, which were illuminated by another pinhole lit by a bright source. This setup ensured that the waves from S1 and S2, derived from the same original source, remained coherent due to any phase changes in the source reflecting similarly in both S1 and S2.

Question 44

What kind of interference fringes do spherical waves emanating from S1 and S2 produce?

Answer 44

The interference fringes produced are visible on the screen GG’, showing both bright and dark regions.

Question 45

How can the positions of maximum and minimum intensities of interference fringes be calculated?

Answer 45

The positions of maximum and minimum intensities can be calculated using the formulas:

For constructive interference resulting in a bright region: x = xn = nλD/d; where n = 0, ±1, ±2, …
For destructive interference resulting in a dark region: x = xn = (n + 1/2)λD/d; where n = 0, 1, 2, …

Question 46

What are the dark and bright bands appearing on the screen called?

Answer 46

The dark and bright bands appearing on the screen are called fringes.

Question 47

Who was Thomas Young?

Answer 47

Thomas Young was an English physicist, physician, and Egyptologist.

Question 48

What were some areas of scientific inquiry that Thomas Young worked on?

Answer 48

Thomas Young worked on a wide variety of scientific problems, including the structure of the eye, the mechanism of vision, and the decipherment of the Rosetta stone.

Question 49

What theory did Thomas Young revive regarding light?

Answer 49

Thomas Young revived the wave theory of light.

Question 50

What did Thomas Young recognize interference phenomena as proof of?

Answer 50

Thomas Young recognized interference phenomena as proof of the wave properties of light.

Question 51

What is the phenomenon observed when closely examining the shadow cast by an opaque object near the region of geometrical shadow?

Answer 51

The phenomenon observed is diffraction, characterized by alternate dark and bright regions similar to interference patterns.

Question 52

What types of waves exhibit diffraction?

Answer 52

Diffraction is a general characteristic exhibited by all types of waves, including sound waves, light waves, water waves, and matter waves.

Question 53

Why do we typically not encounter diffraction effects of light in everyday observations?

Answer 53

We typically do not encounter diffraction effects of light in everyday observations because the wavelength of light is much smaller than the dimensions of most obstacles.

Question 54

What limits the finite resolution of our eyes or optical instruments such as telescopes or microscopes?

Answer 54

The finite resolution of our eyes or optical instruments is limited due to the phenomenon of diffraction.

Question 55

How are colours seen when viewing a CD related to diffraction?

Answer 55

The colours seen when viewing a CD are due to diffraction effects.

Question 56

What is observed when a single narrow slit is illuminated by a monochromatic source?

Answer 56

A broad pattern with a central bright region surrounded by alternate dark and bright regions is observed.

Question 57

How is the intensity pattern of light distributed when a parallel beam of light falls normally on a single slit?

Answer 57

The intensity pattern has a central maximum at zero angle and secondary maxima at angles given by θ= n+1/2/a, where n is an integer and a is the width of the slit.

Question 58

According to Richard Feynman, how does he define the difference between interference and diffraction?

Answer 58

Richard Feynman stated that there is no specific, important physical difference between interference and diffraction, and the distinction is merely a question of usage.

Question 59

What is the pattern observed on the screen in the double-slit experiment a superposition of?

Answer 59

The pattern observed on the screen in the double-slit experiment is a superposition of single-slit diffraction from each slit or hole, and the double-slit interference pattern.

Question 60

What equipment is needed to observe the single-slit diffraction pattern?

Answer 60

Two razor blades and one clear glass electric bulb with a straight filament are needed to observe the single-slit diffraction pattern.

Question 61

How can one create the necessary slit for observing the single-slit diffraction pattern?

Answer 61

Hold the two razor blades so that the edges are parallel and have a narrow slit in between, preferably using the thumb and forefingers.

Question 62

What role does the filament of the bulb play in the experiment to observe the single-slit diffraction pattern?

Answer 62

The filament of the bulb acts as the first slit in the experiment to observe the single-slit diffraction pattern.

Question 63

How can the fringes in the single-slit diffraction pattern be made clearer?

Answer 63

Using a filter for red or blue light can make the fringes in the single-slit diffraction pattern clearer.

Question 64

What principle is consistent with the redistribution of light energy observed in interference and diffraction?

Answer 64

The principle of conservation of energy is consistent with the redistribution of light energy observed in interference and diffraction.

Question 65

What is the equation describing a wave propagating in the +x direction?

Answer 65

The equation describing a wave propagating in the +x direction is y(x,t)=asin(kx−ωt), where a represents the amplitude, ω is the angular frequency, k is the wave number, and λ represents the wavelength.

Question 66

Define the terms a, ω, k, and λ in the context of wave propagation.

Answer 66

In the context of wave propagation, a represents the amplitude, ω represents the angular frequency (equal to 2π times the frequency), k is the wave number (related to the wavelength λ through 2π/k=λ), and λ represents the wavelength.

Question 67

What type of wave is described when the displacement is at right angles to the direction of propagation?

Answer 67

When the displacement is at right angles to the direction of propagation, it describes a transverse wave.

Question 68

What is meant by a “y-polarised wave”?

Answer 68

A “y-polarised wave” refers to a wave where the displacement is in the y direction.

Question 69

How is a linearly polarised wave defined?

Answer 69

A linearly polarised wave is defined as a wave where each point on the string moves on a straight line, and the displacement is always perpendicular to the direction of propagation.

Question 70

Describe the characteristics of a plane polarised wave.

Answer 70

A plane polarised wave is confined to the x−y plane, and its displacement is always perpendicular to the direction of propagation.

Question 71

How can a z-polarised wave be generated?

Answer 71

A z-polarised wave can be generated by considering the vibration of a string in the x−z plane.

Question 72

What is the distinguishing feature of unpolarised waves?

Answer 72

Unpolarised waves have a randomly changing displacement with time, although it is always perpendicular to the direction of propagation.

Question 73

How are transverse waves defined in the context of light waves?

Answer 73

In the context of light waves, transverse waves are defined as waves where the electric field associated with the wave is perpendicular to the direction of propagation.

Question 74

Explain the function of a polaroid in demonstrating the transverse nature of light waves.

Answer 74

A polaroid demonstrates the transverse nature of light waves by selectively allowing only the electric vectors aligned with its molecules to pass through, thus polarising the light along a specific direction perpendicular to the aligned molecules.