1.Explain clearly the difference between interference and diffraction.

Interference	Diffraction
Produced by superposition of light waves from two or more coherent sources.	Produced by superposition of wavelets originating from different parts of the same wavefront.
Requires two coherent sources.	Can be produced by a single slit or obstacle.
Bright fringes are of equal intensity when amplitudes are equal.	Central maximum is brightest and widest.
Fringes are equally spaced.	Fringes are not equally spaced.
All bright fringes have nearly equal width.	Central maximum is twice as wide as the secondary maxima.
Example: Young's double slit experiment.	Example: Fraunhofer diffraction at a single slit.

{Source:- www.learn-fo.com}

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website. Email:- learnfo25@gmail.com

2. What is the difference between holography and photography? (Mark:- 2)

Holography	Photography
Records both amplitude and phase information of light.	Records only intensity (amplitude) information.
Produces a three-dimensional image.	Produces a two-dimensional image.
Uses coherent laser light.	Ordinary light can be used.
Entire image information is stored in every part of the hologram.	Each part of the photograph contains information only about that portion of the object.
Depth and parallax can be observed.	No depth perception is obtained.

{Source:- www.learn-fo.com}

3. What is the radius of 1st zone of a zone plate of focal length 0.2 m for a light of wavelength 5000 Å? (Mark:- 2)

Given:

For the first Fresnel zone,

Answer:

{Source:- www.learn-fo.com}

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website.Email:- learnfo25@gmail.com

4. Distinguish between Fresnel and Fraunhofer type of diffraction.(Mark:- 4)

Fresnel Diffraction	Fraunhofer Diffraction
Source and screen are at finite distances from the diffracting aperture.	Source and screen are effectively at infinite distances from the diffracting aperture.
No lenses are required.	Convex lenses are generally used to obtain parallel rays and focus the diffraction pattern.
Incident wavefront is spherical.	Incident wavefront is plane.
Diffracted wavefront is spherical.	Diffracted wavefront is plane.
Pattern changes with the distance between aperture and screen.	Pattern is independent of the distance between aperture and screen.
Mathematical analysis is comparatively complicated.	Mathematical analysis is comparatively simple.
Fringes are not sharp and well defined.	Fringes are sharp and well defined.
Example: Diffraction near the edge of an obstacle.	Example: Single slit Fraunhofer diffraction pattern.

5.Discuss the phenomenon of diffraction at a straight edge and state how you would determine the wavelength of light from the study of the fringes. (Mark:- 4)

When light passes close to a straight sharp edge, it bends slightly into the geometrical shadow region. This bending of light from its rectilinear path is known as diffraction at a straight edge.

Consider a monochromatic source S illuminating a straight edge AB. A screen is placed beyond the edge to observe the diffraction pattern.

According to Huygens' principle, every point of the unobstructed wavefront acts as a source of secondary wavelets. The wavelets reaching a point near the edge interfere with one another and produce alternate bright and dark bands near the boundary of the geometrical shadow.

The intensity does not fall abruptly at the geometrical shadow. Instead, a system of diffraction fringes is observed.

The bright and dark bands become closer together as the distance from the edge increases and their intensity gradually decreases.

To determine the wavelength of light, let

• a = Distance between source and straight edge
• b = Distance between straight edge and screen
• x_n = Distance of the nth fringe from the geometrical boundary
• λ = Wavelength of light

For diffraction at a straight edge, the position of the nth fringe is given by

Hence,

The distances of the fringes from the geometrical shadow boundary are measured experimentally using a travelling microscope.

Knowing the values of a, b and x_n, the wavelength λ of the monochromatic light can be calculated from the above relation.

Thus, diffraction at a straight edge produces alternate bright and dark fringes near the shadow boundary, and the wavelength of light can be determined by measuring the fringe positions.

{Source:- www.learn-fo.com}

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website.Email:- learnfo25@gmail.com

6. What is the fundamental principle of hologram? How is it produced and how is the image reconstructed from it?

A hologram is a photographic record of the interference pattern produced by the superposition of two coherent light waves. The science of recording and reproducing three-dimensional images by this method is called holography.

The fundamental principle of holography is interference and diffraction of coherent light. Unlike ordinary photography, a hologram records both the amplitude and phase information of light reflected from an object.

Principle of Holography:

When a coherent laser beam is divided into two parts, one beam illuminates the object and the other acts as a reference beam. The light reflected from the object interferes with the reference beam and forms an interference pattern on a photographic plate. This recorded pattern is called a hologram.

Production of a Hologram:

1. A monochromatic coherent laser source is used.
2. The laser beam is divided into two parts by a beam splitter.
3. One part is directed towards the object and is called the object beam.
4. The second part reaches the photographic plate directly and is called the reference beam.
5. The object beam reflected from the object interferes with the reference beam.
6. The resulting interference pattern is recorded on a photographic plate.
7. After development, the photographic plate becomes the hologram.

Reconstruction of the Image:

1. The developed hologram is illuminated with the same laser beam used during recording.
2. The hologram behaves like a complex diffraction grating.
3. Light diffracted by the hologram reconstructs the original wavefront coming from the object.
4. An observer sees a virtual three-dimensional image of the object at its original position.
5. A real image may also be formed on the opposite side of the hologram.

Advantages of Holography:

• Produces a three-dimensional image.
• Records both amplitude and phase information.
• Provides depth and parallax.
• Even a small part of the hologram can reproduce the whole image.

Thus, holography is based on the recording of interference patterns produced by coherent light and the reconstruction of the original wavefront through diffraction, resulting in a three-dimensional image.

{Source:- www.learn-fo.com}

7. What is the meaning of half period zones? Why are they called so? How are they constructed?

According to Fresnel's theory of diffraction, the wavefront reaching a point can be divided into a number of concentric regions called half period zones.

A half period zone is defined as the region of a wavefront such that the path difference between light coming from the boundaries of two successive zones is equal to half the wavelength (λ/2).

Thus, if the path difference between the contributions from two adjacent zones is λ/2, the corresponding phase difference is π radians (180°).

Why are they called Half Period Zones?

The time taken by light to travel a path difference of λ/2 is equal to half of its time period. Therefore, the waves arriving from successive zones differ in phase by half a period.

Hence these zones are called half period zones.

Construction of Half Period Zones:

Consider a wavefront AB and a point P where the resultant illumination is to be calculated.

1. Join the point P to the centre O of the wavefront.
2. With P as centre, draw spheres of radii

and so on.

The spheres cut the wavefront into a series of concentric circular rings.

These rings are called the first, second, third, fourth, etc., half period zones.

The path difference between light coming from the boundaries of two successive zones is λ/2 and therefore the phase difference is π radians.

The contributions from successive zones tend to cancel each other partially, which forms the basis of Fresnel's diffraction theory.

Thus, half period zones are concentric regions of a wavefront whose successive boundaries differ in path by λ/2, and they are constructed by drawing spheres centred at the observation point with radii increasing by λ/2.

{Source:- www.learn-fo.com}

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website.Email:- learnfo25@gmail.com

8. State the basic difference between a conventional photograph and a hologram.

A conventional photograph records only the intensity (amplitude) distribution of light and produces a two-dimensional image.

A hologram records both the amplitude and phase information of light and reconstructs a three-dimensional image.

{Source:- www.learn-fo.com}

9. Explain Fresnel's half-period zones for plane waves.

Fresnel divided a plane wavefront into a number of concentric regions called half-period zones.

These zones are constructed so that the path difference between light coming from the boundaries of two successive zones is

Hence, the phase difference between waves from successive zones is

They are called half-period zones because a path difference of λ/2 corresponds to a phase difference of half a cycle.

The secondary wavelets from successive zones partially cancel one another, and the resultant disturbance at a point is obtained by adding the contributions of all the zones.

{Source:- www.learn-fo.com}

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website.Email:- learnfo25@gmail.com

10. What is zone plate? How is it constructed? Explain its theory and compare its working to that of a convex lens.

Zone Plate

A zone plate is a circular optical device consisting of alternate transparent and opaque concentric rings called Fresnel zones. It focuses light by the phenomenon of diffraction rather than refraction.

Construction of a Zone Plate

A plane sheet of glass is divided into a number of concentric circular zones known as Fresnel half-period zones.

The alternate zones are made opaque while the remaining zones are kept transparent. Usually, the odd zones are transparent and the even zones are opaque.

The radii of the zones are given by

rn = √(nλf)

where,
rn = radius of nth zone
λ = wavelength of light
f = focal length of the zone plate
n = zone number

Theory of Zone Plate

When a plane wavefront falls on a zone plate, each transparent zone acts as a secondary source of wavelets according to Huygens' principle.

The waves reaching the point on the axis from successive zones differ in phase by π (180°).

In a complete wavefront, the contributions from successive zones tend to cancel each other. By making alternate zones opaque, the destructive interference is removed and the amplitudes from the transparent zones add together.

As a result, a point of maximum intensity is obtained on the axis, which acts as the principal focus of the zone plate.

The principal focal length of a zone plate is

f = r1² / λ

where r1 is the radius of the first zone.

A zone plate possesses several foci:

f, f/3, f/5, f/7, ...

These are called odd-order foci.

Comparison Between Zone Plate and Convex Lens

Zone Plate	Convex Lens
Works on diffraction and interference.	Works on refraction.
Consists of alternate transparent and opaque zones.	Consists of transparent refracting material.
Has multiple foci (f, f/3, f/5...).	Has only one principal focus.
Intensity at focus is comparatively low.	Produces brighter images.
Suffers from chromatic aberration strongly.	Chromatic aberration can be minimized.
Focusing is due to diffraction.	Focusing is due to refraction.

Conclusion

A zone plate is a diffraction device made of alternate transparent and opaque Fresnel zones. It focuses light by interference and diffraction, whereas a convex lens focuses light by refraction.

{Source:- www.learn-fo.com}

11. Explain the principle of holography. How can a hologram be recorded? Explain the formation of real and virtual images from a recorded hologram.

Holography

Principle of Holography

Holography is a technique used to record and reproduce the complete three-dimensional information of an object. Unlike ordinary photography, which records only the intensity of light, holography records both the amplitude and phase of light waves reflected from the object.

The principle of holography is based on the phenomenon of interference and diffraction of coherent light. A highly coherent laser beam is divided into two parts:

• Object Beam – illuminates the object and carries information about it.
• Reference Beam – reaches the recording plate directly.

The interference between the object beam and reference beam produces an interference pattern on a photographic plate. This recorded pattern is called a hologram.

Recording of a Hologram

The recording process involves the following steps:

1. A monochromatic laser beam is used as the light source.
2. The laser beam is split into two beams using a beam splitter.
3. One beam acts as the object beam and illuminates the object.
4. The light reflected from the object reaches the photographic plate.
5. The second beam acts as the reference beam and falls directly on the same photographic plate.
6. The object beam and reference beam interfere with each other.
7. The resulting interference fringes are recorded on the photographic plate.
8. After chemical processing, the photographic plate becomes a hologram.

Reconstruction of Image from a Hologram

To reconstruct the image, the developed hologram is illuminated with a laser beam identical to the reference beam used during recording. The hologram behaves like a diffraction grating and reconstructs the original wavefront of the object.

Formation of Virtual Image

When the hologram is illuminated by the reference beam, one of the diffracted waves reproduces the original object wavefront.

The observer looking through the hologram sees a three-dimensional image located at the original position of the object. This image cannot be projected on a screen and is therefore called a virtual image.

Formation of Real Image

Another diffracted wave produced by the hologram converges to form an image in front of the hologram.

This image can be projected onto a screen and is known as the real image. It appears on the opposite side of the hologram from the virtual image.

Advantages of Holography

• Produces true three-dimensional images.
• Stores both amplitude and phase information.
• Provides depth and parallax effects.
• Each part of a hologram contains information about the whole object.

Conclusion

Holography is based on the interference of coherent light waves. A hologram is recorded by the interference of object and reference beams. When illuminated by the reference beam, the hologram reconstructs both virtual and real three-dimensional images of the original object.

{Source:- www.learn-fo.com}

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website.Email:- learnfo25@gmail.com

14. Discuss similarities between a Zone Plate and a Convex Lens.

• Both are used to focus light rays.
• Both produce real and virtual images.
• Both possess a principal focus and focal length.
• Both can form images of objects placed at different distances.
• Both converge parallel rays to a focal point.
• Both are used in optical imaging systems.

{Source:- www.learn-fo.com}

15. Discuss the difference between Interference and Diffraction Pattern.

Interference	Diffraction
Produced by superposition of light from two or more coherent sources.	Produced by superposition of light from different parts of the same wavefront.
Fringes are equally spaced.	Fringes are not equally spaced.
Bright fringes have nearly equal intensity.	Central maximum is brightest and widest.
Requires two coherent sources.	Requires only one slit or aperture.
Fringe width is uniform.	Fringe width varies from one fringe to another.

{Source:- www.learn-fo.com}

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website.Email:- learnfo25@gmail.com

16. Write very briefly on Hologram.

A hologram is a photographic record of the interference pattern produced by the interaction of an object beam and a reference beam of coherent light. It contains both amplitude and phase information of the light wave. When illuminated by a suitable laser beam, it reconstructs a three-dimensional image of the original object.

{Source:- www.learn-fo.com}

18. Give an expression for Fresnel diffraction pattern of a straight edge.

Fresnel Diffraction at a Straight Edge

Introduction

Fresnel diffraction occurs when either the source of light or the screen (or both) is at a finite distance from the diffracting obstacle. The wavefront reaching the obstacle is therefore spherical rather than plane. A straight edge is one of the simplest examples of Fresnel diffraction.

When a monochromatic light source illuminates a straight opaque edge, the geometrical shadow is not perfectly dark. Instead, alternate bright and dark bands are observed near the boundary of the shadow due to the interference of secondary wavelets originating from different parts of the wavefront.

Theory

Consider a point source S illuminating a straight edge. Let P be a point on the observation screen. According to Huygens-Fresnel principle, every point on the unobstructed wavefront acts as a source of secondary wavelets.

The amplitude at P is obtained by summing the contributions from all the unobstructed portions of the wavefront. Since different portions of the wavefront have different path lengths to P, they arrive with different phases and interfere with one another.

To simplify the calculation, the wavefront is divided into a large number of Fresnel half-period zones. The resultant amplitude is obtained using Fresnel integrals.

Expression for the Amplitude

The resultant complex amplitude at a point P is

A = C(u) + iS(u)

where

C(u) = ∫₀ᵘ cos(πt²/2) dt

and

S(u) = ∫₀ᵘ sin(πt²/2) dt

These functions are known as Fresnel cosine and Fresnel sine integrals. The parameter u is called the reduced distance parameter and depends on the position of the observation point relative to the edge.

Expression for Intensity

Since intensity is proportional to the square of the amplitude,

I = I₀ [C²(u) + S²(u)]

where

• I = intensity at the observation point
• I₀ = intensity of the incident light
• C(u) and S(u) are Fresnel integrals

Nature of the Diffraction Pattern

The diffraction pattern consists of alternate bright and dark bands near the geometrical shadow boundary.

• The fringes are not equally spaced.
• The intensity decreases gradually away from the edge.
• The first bright fringe is brighter than the others.
• Inside the geometrical shadow, some light is present due to diffraction.
• Far from the edge, the intensity approaches that of the incident light.

Conclusion

The Fresnel diffraction pattern of a straight edge arises due to the interference of secondary wavelets from the unobstructed portion of the wavefront. The resultant amplitude is expressed in terms of Fresnel integrals:

A = C(u) + iS(u)

and the intensity distribution is given by

I = I₀ [C²(u) + S²(u)].

This explains the formation of bright and dark diffraction bands near the edge of the geometrical shadow.

{Source:- www.learn-fo.com}

Derive the expression for the phase difference between two points in a wavefront due to the presence of a half-period zone. How is it related to the distances of points from the boundary of the zone?

Phase Difference Between Two Points Due to a Half-Period Zone

Introduction

According to Fresnel's theory of diffraction, a wavefront can be divided into a number of concentric regions known as Fresnel half-period zones. These zones are constructed so that the path difference between light coming from the boundaries of two successive zones is equal to half the wavelength of light.

Derivation

Let P be the point of observation and let O be the center of the wavefront. Consider two successive boundaries A and B of Fresnel half-period zones.

If the distances of A and B from P are r₁ and r₂ respectively, then by definition of a half-period zone,

r₂ − r₁ = λ/2

where λ is the wavelength of light.

The phase difference corresponding to a path difference Δ is given by

φ = (2π/λ)Δ

Substituting Δ = λ/2,

φ = (2π/λ)(λ/2)

φ = π radians

or

φ = 180°

Hence, the phase difference between disturbances arriving from two successive half-period zones is π radians.

Relation with Distance from the Boundary of the Zone

Let r₀ be the distance from the center O of the wavefront to the observation point P.

For the nth zone boundary,

rₙ − r₀ = nλ/2

where n = 1, 2, 3, ...

Thus, the distances of successive zone boundaries from the observation point increase by λ/2.

Therefore, each successive zone contributes a phase change of π radians with respect to the previous zone.

As a result, the contributions from successive zones are nearly opposite in phase and tend to cancel one another.

Conclusion

The path difference between two successive Fresnel half-period zones is λ/2. Therefore, the phase difference is

φ = π radians = 180°

The distance of the nth zone boundary from the observation point is related by

rₙ − r₀ = nλ/2

showing that successive zone boundaries differ in path length by λ/2 and hence in phase by π radians.

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website.Email:- learnfo25@gmail.com

20. What are Fresnel’s Half-Period Zones?

Fresnel's half-period zones are imaginary concentric circular regions into which a wavefront is divided such that the path difference between light coming from successive zones to a point is λ/2.
Properties:
Each zone contributes nearly equal amplitude.
Successive zones differ in phase by π (180°).
Their contributions partially cancel each other.
Used to explain diffraction phenomena.

21. What is a Zone Plate? What are the Two Types of Zone Plate?

22. Distinguish Between a Convex Lens and a Zone Plate

23. Describe the theory of zone plate. Determine the radius of the first zone of a zone plate of focal length 20 cm for incident light of wavelength 5000 Å.

{Source:- www.learn-fo.com}

Follow Us

Note: If you have any previous year question paper solutions, please provide them to us. We will mention your name on our website.Email:- learnfo25@gmail.com

24. What types of information of the object are recorded in a hologram? Distinguish between a conventional photograph and a hologram. Explain how recording and reconstruction of a hologram of an object is done using a beam of laser light.

{Source:- www.learn-fo.com}