#
KTU Previous Question Paper 2016 with answers for Engineering Physics** ****
**

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**FIRST SEMESTER B.TECH DEGREE EXAMINATION, JANUARY 2016**
**Course Name: ENGINEERING PHYSICS**
Max.Marks:100 Duration: 3 Hours
**Part A**
*Answer ALL questions each carries 2 marks*
- What do you mean by quality factor of an oscillator?
- What is the relation between path difference and phase difference in wave motion?
- Two independent source of light can not produce interference fringes. Why?
- Define dispersive power of a grating.
- Distinguish between plane polarized light and unpolarized light.
- What is Miessner effect?
- What is phase space?
- What is the probability interpretation of wave function?
- What is the relation connecting reverberation time and total absorption?
- What is magnetostriction effect?
- Write any two advantage of Hologram over photographic images.
- Distinguish between step index fiber and Graded index fiber.

**PART B**
*Answer any 10 questions. Each question carries 4 marks*
13. Compare an electrical and mechanical oscillator.

14. A transverse wave on a stretched string is described by y(x,t)=4 sin(25t+0.016+π/3) where x and y are in cm and t in second. Obtain the **(i)**speed **(ii)**amplitude **(iii) **frequency and **(iv)** Initial phase at the origin.
15. Newton’s ring arrangement n^{th} dark ring formed by light of wavelength 6000 A^{0}coincides with (n+1)^{th} dark ring for light of wavelength 4500 A^{0}. If the radius of curvature of convex surface is 90cm, find the diameter of the n^{th} ring for light of wavelength 6000 A^{0}.
16. A plane transmission grating has 6000 lines/cm. Find the angular separation between two wavelengths 500nm and 510nm in the 3^{rd} order.
17. The refractive index of a calcite is 1.658 for ordinary ray and it is 1.486 for extraordinary ray. A slice having thickness 0.9×10^{-4}cm is cut from the crystal. For what wavelength the slice will acts as a **(i) **Quarter wave plate. **(ii) **Half wave plate.
18. Distinguish between Type I and Type II superconductors with examples.
19. Calculate the De Broglie wavelength of electron whose kinetic energy is 10Kev.
20. Distinguish between Macrostate and Microstate of a system.
21. The volume of a hall is 3000 m^{3 }. It has a total absorption of 100m^{2} sabine. If the hall is filled with audience who add another 80m^{2} sabine, then find the difference in reverberation time.
22. What is NDT? and how ultrasonic wave used for NDT?
23. What is the difference between spontaneous emission and stimulated emission?
24. What is LED? Give its working principle?
**PART C**
**Answer any 3 Questions each carries 6 marks.**
25. Considering the transverse vibration in a stretched string, derive the differential equation of one dimensional wave.
26. Light from a monochromatic source is allowed to fall on a single slit. Two lenses are given. With the help of neat diagram write the experimental set up for obtaining the diffraction pattern. Deduce the condition for getting bright and dark regions on the screen. Also obtain the width of central maximum.
27. How a Nicol prism can be constructed from a calcite crystal? How can be it be used as polarizer and as a analyzer?
28. Formulate a Schrodinger’s time dependent equation starting from a plane wave equation by using a de Broglie’s formula and Einstein’s relation for photon Energy.
**PART D**
**Answer any 3 Questions. Each Question carries 6 marks**
29. With a neat diagram explain how ultrasonic waves are produced by piezoelectric oscillator.
30. What are the factors affecting acoustics of a building?
31. Outline the principle and working of Ruby Laser.
32. Define numerical aperture of an optical fiber and derive an expression for NA of step index fibre.
**KTU Previous Question Paper 2016 with answers for Engineering Physics**
**ANSWERS**
**1. What do you mean by quality factor of an oscillator?**
**ANS:**
Quality factor **(Q)** of an oscillator is defined as 2Π times the ratio of energy stored to the average energy loss per period.
**2.What is the relation between path difference and phase difference in wave motion?**
**ANS:**
A path difference of x_{0} will correspond to a phase difference of
**3.Two independent source of light can not produce interference fringes. Why?**
**ANS:**
Two sources of light with same wavelength and amplitude with a constant phase difference is called coherent sources.
Only coherent sources can produce interference pattern. Two independent sources can never be mutually coherent.
**4.Define dispersive power of a grating.**
**ANS:**
Dispersive power of grating is defined by the ratio of change in angle of diffraction to corresponding change in wave length. Dispersive power of grating is given by
**5.Distinguish between plane polarized light and unpolarized light.**
**ANS:**
• Un-polarized light has electrical component in every direction, at any given time, but the polarized light has the electric component only in one direction for a given time.
• When the un-polarized light is polarized, it is always reduced in intensity.
**6.What is Meissner effect ?**
**Ans: **
When a superconductor is placed in a magnetic field, that superconductor expels magnetic flux completely, a property of superconductors which has come to be known as Meissner effect.

**7.What is phase space?**
**ANS:**
Phase-space is such a space, a point in which represents a micro-state of the system. The 2f-dimensional space with f generalized position co-ordinates and f generalized momenta is called a phase space.
**8.What is the probability interpretation of wave function?**
**ANS:**
If a particle exists in a given region of space, the total probability of finding the particle in that region is one. Mathematically,
**∫Ψ*Ψdτ=1**
where dτ is the volume element
Ψ*Ψ represents probability density
**9.What is the relation connecting reverberation time and total absorption?**
**ANS:**
**Reverberation Time **is the time it takes the sound to decay away 60 dBs.
__Sabine’s formula__
T = 0.16 V / A
where V is the room volume in cubic meters, and A is the total absorption in square meters.
**10.What is magnetostriction effect?**
**ANS:**
Magnetostriction effect is the property of a ferromagnetic materials (iron, nickel) that causes them to change their shape and dimensions when they are kept in a magnetic field.
**11.Write any two advantage of Hologram over photographic images.**
**ANS:**
In hologram we have the freedom of vision to change the view point and the focus, while we see a three dimensional object i.e. we have a 3D view ( Stereoscopic vision). A hologram records both intensity and phase variations.
A photograph is a two dimensional version of a 3D object i.e. it is a still of a 3D scene, with fixed viewpoint and focus. Thus there is no stereoscopic vision. A photographic plate is sensitive to only the intensity variation and not the phase variations.
**12.Distinguish between step index fiber and Graded index fiber.**
**ANS:**
**PART B**
*Answer any 10 questions. Each question carries 4 marks*
**13.Compare an electrical and mechanical oscillator.**
**ANS:**
**Electrical oscillator**
An oscillator can be defined as an electronic circuit which converts dc power from the supply to ac power in the load. It is circuit which generates an output signal without any external input signal.
**Mechanical Oscillator**
In mechanical oscillator there is only a transformation from K.E to P.E and vice versa. Total Energy of a harmonic oscillator with no dissipative forces remains constant.
**14. A transverse wave on a stretched string is described by y(x,t)=4.0sin(25t+0.016x+π/3) where x and y are in cm and t is in second.**

**Obtain the (i) Speed (ii) Amplitude (iii) Frequency and(iv)Initial phase at the origin.**
**ANS:**
**(i)** Instantaneous velocity is,
**(ii) **amplitude is 4
**(iii) **Frequency,
**ω=2πf**
**f=ω/2π**
where, **ω=25;**
**f=25/2π;**
**=3.98Hz**
**(iv) **Initial phase at origin is, **π/3**
**15. With Newton’s rings arrangement, nth dark ring formed by light of wavelength 6000 A° coincides with the (n+1)th dark ring for light of wavelength ***4500A°. *If the radius of curvature of the convex surface is 90 cm, find the diameter of the nth ring for light wavelength 6000 A°.
**ANS:**
We know that,
for dark ring
**2t=nλ**; n^{th} dark ring of first wave coincide with (n+1)^{th} dark ring;
So, **nλ**_{1}=(n+1)λ_{2}
**n** x **6000=(n+1)** x **4500 **by solving we get,
**n=3**
We know that,
**r**_{n}^{2}=Rnλ
**r**_{n=√Rnλ}
r=√(90×10^{-2}x3x6000x10^{-10})
r=1.272mm.
**16. A plane transmission grating has 6000 lines/cm. Find the angular separation between two wavelengths 500nm and 510nm in the 3**^{rd} order.
**ANS:**
We know that;
SinΘ=Nnλ
N be the number of lines in one metre of the grating
Θ_{1}=Sin^{-1}(6000x100x3x500x10^{-9})
Θ_{1}=64.16^{o}
Θ_{2}=Sin^{-1}(6000x100x3x510x10^{-9})
Θ_{2}=66.64^{o}
angular separation= **Θ**_{2 }– Θ_{1}
**=2.48**^{o}
**17. The refractive index of a calcite is 1.658 for ordinary ray and it is 1.486 for extraordinary ray. A slice having thickness 0.9×10**^{-4}cm is cut from the crystal. For what wavelength the slice will acts as a (i) Quarter wave plate. (ii) Half wave plate.
**ANS:**
**(i) **For Quarter Wave Plate, thickness
**(ii) **For Half wave plate, thickness
**18. Distinguish between Type I and Type II superconductors with examples.**
**ANS:**

**Type I Superconductors****Type II Superconductors**
1. Soft superconductors are those which can tolerate impurities without affecting the superconducting properties. 1. Hard superconductors are those which cannot tolerate impurities, i.e., the impurity affects the superconducting property.
2. They have low critical field. 2. They have high critical field.
3. Show complete Meissner effect.

3. Hard super conductors trap magnetic flux and hence Meissner effect is not complete.
4. The current flows through the surface only. 4. It is found that current flows throughout the material.
5. Eg. Tin, Aluminum 5. Eg. Tantalum, Neobium

**19. Calculate the De Broglie wavelength of electron whose kinetic energy is 10Kev.**
**ANS:**
Kinetic Energy **KE=1/2(mv**^{2})
**λ=h/p**
**2Em=P**^{2}
P=√(2Em)
λ=h/√(2Em)
1eV=1.6×10^{-19}J ; mass of e=9.1×10^{-31}kg ; h=6.626×10^{-34} m^{2}kg/s
Substituting the value we get,
λ=1.22nm.
**20. Distinguish between Macrostate and Microstate of a system.**
**ANS:**
**Macrostate and Microstate**
The state of a physical system characterized by its bulk parameters like pressure, volume, temperature, mass etc. is called **Macro states.**
A **Microstate ** of a system is characterized by the value of coordinates of position and momentum for all particle on a system at any instant.
Microstate changes with time without affecting the Macrostates. Thus an enormously large number of microstates correspond to each macrostate of the system.
**21. The volume of a hall is 3000 m**^{3 }. It has a total absorption of 100m^{2} sabine. If the hall is filled with audience who add another 80m^{2} sabine, then find the difference in reverberation time.
**ANS:**
We know Sabine’s formula;
T = 0.16 V / A
Here,
V- volume
A- area of absorption
reverberation time T_{1}= 0.16×3000/100
**=4.8 Sec**
T_{2}=0.16×3000/180
**=2.67 Sec**
difference in reverberation time,
**T**_{2} – T_{1}
**=2.13 Sec**
**22. What is NDT? and how ultrasonic wave used for NDT?**
**ANS:**
Nondestructive testing is a method of finding defects in an object without harming the object. NDT is used to look for internal changes or signs of wear on airplanes. Discovering defects will increase the safety of the passengers. The railroad industry also uses nondestructive testing to examine railway rails for signs of damage. Sound with high frequencies, or **ultrasound**, is one method used in NDT. Basically, ultrasonic waves are emitted from a transducer into an object and the returning waves are analyzed. If an impurity or a crack is present, the sound will bounce off of them and be seen in the returned signal. In order to create ultrasonic waves, a transducer contains a thin disk made of a crystalline material with piezoelectric properties, such as quartz. When electricity is applied to piezoelectric materials, they begin to vibrate, using the electrical energy to create movement. Remember that waves travel in every direction from the source. To keep the waves from going backwards into the transducer and interfering with its reception of returning waves, an absorptive material is layered behind the crystal. Thus, the ultrasound waves only travel outward.
**23. What is the difference between spontaneous emission and stimulated emission?**
**ANS:**
**spontaneous emission**
The emission of photons by the natural de-excitation transition of atoms, molecules, ions etc. is known as spontaneous emission process. This is an uncontrolled and natural phenomenon in which each excited atom emit photons independently in random direction, phase and polarization.
**stimulated emission**
The process of de-excitation transition with the emission of radiation on finding an identical radiation as stimuli to trigger the emission process and is known stimulated emission.
**24. What is LED? Give its working principle?**
**ANS:**
LED operating on the principle of injection of luminescence. Basically LED is a semiconductor pn junction device capable of emission of electromagnetic radiation under forward-biased condition. LED emits light under forward biased condition. When the external voltage exceeds the barrier potential, recombination between electrons and holes take place. The minority carrier concentration on both sides of the junction are considerably increased under this condition, which increases their rate of recombination. Thus electromagnetic radiation emitted.
**PART C**
**Answer any 3 Questions each carries 6 marks.**
**25. Considering the transverse vibration in a stretched string, derive the differential equation of one dimensional wave.**
**ANS:**
**Ans:**
When a string stretched btween A and B is plucked, let tension acts at P&Q which are a
**26. Light from a monochromatic source is allowed to fall on a single slit. Two lenses are given. With the help of neat diagram write the experimental set up for obtaining the diffraction pattern. Deduce the condition for getting bright and dark regions on the screen. Also obtain the width of central maximum.**
**ANS:**
**Fraunhofer Diffraction**
The source and screen are moved to large distance from the diffracting aperture. This limiting case is called Fraunhofer diffraction. Fraunhofer conditions can be established in the laboratory by using two converging lenses.
The first lens converts the diverging wave from the source into a plane wave. The second lens converges the waves leaving the aperture to a point P.
Consider a narrow slit AB of width ‘a’ on which monochromatic light of wavelength ‘λ’ is falling from a collimating lens L. The wavefront incident on the slit AB is plane. Let the light emerging from AB be incident on another lens L’.
The path difference between wavelets from A and B is AL=AB SinΘ=a SinΘ, where ‘a’ is the width of the slit and Θ is the angle which the diffracted beam makes with the direction OP.
If the path difference between wavelets from A and B is λ, i.e, a SinΘ=λ
Path difference between wavelets from A and those from O is λ/2 and they cancel one another. All other pairs of corresponding points in the two halves OA and OB of the wavefront will also differ by a path by λ/2 and cancel each other. Thus dark band will appear at P’
First minimum, on either side of C will appear in a direction Θ
SinΘ=λ/a
direction of the n^{th} minimum is given by
SinΘ_{n}=nλ/a, where n=1,2,3,………etc
Lens L’ has the screen at its focus,
sinΘ=λ/a=x/f
x=fλ/a
x is the distance of the first minimum from C and f is the focal length of lens L’
Hence width of central maximum,
2x=2fλ/a
If AN= 3λ/2
i.e. if a sinΘ’=3λ/2
The direction of the nth secondary maximum is given by
sinΘ’_{n}=(2n+1)λ/2a
where n=1,2,3,…etc.
**27. How a Nicol prism can be constructed from a calcite crystal? How can be it be used as polarizer and as a analyzer?**
**ANS:**
Nicol prism is an optical device made from calcite crystal. This is used in many optical instruments for producing and analyzing polarized light. It removes one of the two refracted rays, usually the O-ray, by total internal reflection.The transmitted E-ray is plane polarized. It is constructed from a calcite crystal whose length is about three times its width.The ends are cut down from 71^{o }in the principal section to a more acute angle of 68^{o}. The crystal is then cut into two pieces diagonally through one of the obtuse corners. The two cut surfaces are polished optically flat and then cemented together in their original position with a transparent cement called canada balsam. Canada balsam is used because its refractive index lies between the refractive indices of calicite for the O and E rays.
Optically the balsam is denser than the calicite for the E-ray and less dense for the O-ray. The E-ray, therefore, will be refracted into the balsam and on through the calcite crystal, whereas the O-ray, for large angles of incidence, will be totally reflected.
Nicol prism can be used as a polarizer and an analyser. It is used in specially constructed microscopes for studying the optical properties of crystals.
**28. Formulate a Schrodinger’s time dependent equation starting from a plane wave equation by using a de Broglie’s formula and Einstein’s relation for photon Energy.**
**ANS:**
The differential equation for a wave associated with a particle and propagating along X- direction may be written as
**PART D**
**Answer any 3 Questions. Each Question carries 6 marks**
**29. With a neat diagram explain how ultrasonic waves are produced by piezoelectric oscillator.**
**ANS:**
**Principle: Inverse piezo electric effect**
• If mechanical pressure is applied to one pair of opposite faces of certain crystals like quartz, equal and opposite electrical charges appear across its other faces. This effect is called as piezo-electric effect.
• The converse of piezo electric effect is also true.
• If an electric field is applied to one pair of faces, the corresponding changes in the dimensions of the other pair of faces of the crystal are produced. This effect is known as inverse piezo electric effect.
Construction The circuit diagram is shown in Figure
• The quartz crystal is placed between two metal plates A and B.
• The plates are connected to the primary (L3) of a transformer which is inductively coupled to the electronics oscillator.
• The electronic oscillator circuit is a base tuned oscillator circuit.
• The coils L1 and L2 of oscillator circuit are taken from the secondary of a transformer T.
• The collector coil L2 is inductively coupled to base coil L1.
• The coil L1 and variable capacitor C1 form the tank circuit of the oscillator. Working
• When H.T. battery is switched on, the oscillator produces high frequency alternating voltages with a frequency.
• Due to the transformer action, an oscillatory e.m.f. is induced in the coil L3. This high frequency alternating voltages are fed on the plates A and B.
• Inverse Piezo-electric effect takes place and the crystal contracts and expands alternatively. The crystal is set into mechanical vibrations.
• The frequency of the vibration is given by
where P = 1,2,3,4 … etc. for fundamental, first over tone, second over tone etc., Y = Young’s modulus of the crystal and ρ = density of the crystal.
• The variable condenser C1 is adjusted such that the frequency of the applied AC voltage is equal to the natural frequency of the quartz crystal, and thus resonance takes place.
• The vibrating crystal produces longitudinal ultrasonic waves of large amplitude.
**30. What are the factors affecting acoustics of a building?**
**ANS:**
**(1) Reverberation: **Reverberation is a desirable property of auditoriums to the extent that it helps to overcome the inverse square law drop off of sound intensity in the enclosure. However, if it is excessive, it makes the sounds run together with loss of articulation – the sound becomes muddy, garbled.
**(2) Loudness: **
(3) Focusing
(4) Echoes
(5) Echelon effect
**(6) Resonance: ** the frequencies of forced vibrations may be the same thus resulting in the resonance. Some times even though the frequency of crated sound is not equal to that of the original sound, they will super pose with each other. Due to their interference the original sound is distorted.
**(7) Noise:** Generally there are three types of noises. They are (i) Air-borne noise (ii) Structure borne noise (iii) Inside noise. The prevention of noise is known as sound insulation or soundproofing. The method of sound insulation depends on the type of noise to be decreased.
**31. Outline the principle and working of Ruby Laser.**
**ANS:**
**32. Define numerical aperture of an optical fiber and derive an expression for NA of step index fibre.**
**ANS:**

**FIRST SEMESTER B.TECH DEGREE EXAMINATION, JANUARY 2016**

**Course Name: ENGINEERING PHYSICS**

Max.Marks:100 Duration: 3 Hours

**Part A**

*Answer ALL questions each carries 2 marks*- What do you mean by quality factor of an oscillator?
- What is the relation between path difference and phase difference in wave motion?
- Two independent source of light can not produce interference fringes. Why?
- Define dispersive power of a grating.
- Distinguish between plane polarized light and unpolarized light.
- What is Miessner effect?
- What is phase space?
- What is the probability interpretation of wave function?
- What is the relation connecting reverberation time and total absorption?
- What is magnetostriction effect?
- Write any two advantage of Hologram over photographic images.
- Distinguish between step index fiber and Graded index fiber.

**PART B**

*Answer any 10 questions. Each question carries 4 marks*
13. Compare an electrical and mechanical oscillator.

14. A transverse wave on a stretched string is described by y(x,t)=4 sin(25t+0.016+π/3) where x and y are in cm and t in second. Obtain the

14. A transverse wave on a stretched string is described by y(x,t)=4 sin(25t+0.016+π/3) where x and y are in cm and t in second. Obtain the

**(i)**speed**(ii)**amplitude**(iii)**frequency and**(iv)**Initial phase at the origin.
15. Newton’s ring arrangement n

^{th}dark ring formed by light of wavelength 6000 A^{0}coincides with (n+1)^{th}dark ring for light of wavelength 4500 A^{0}. If the radius of curvature of convex surface is 90cm, find the diameter of the n^{th}ring for light of wavelength 6000 A^{0}.
16. A plane transmission grating has 6000 lines/cm. Find the angular separation between two wavelengths 500nm and 510nm in the 3

^{rd}order.
17. The refractive index of a calcite is 1.658 for ordinary ray and it is 1.486 for extraordinary ray. A slice having thickness 0.9×10

^{-4}cm is cut from the crystal. For what wavelength the slice will acts as a**(i)**Quarter wave plate.**(ii)**Half wave plate.
18. Distinguish between Type I and Type II superconductors with examples.

19. Calculate the De Broglie wavelength of electron whose kinetic energy is 10Kev.

20. Distinguish between Macrostate and Microstate of a system.

21. The volume of a hall is 3000 m

^{3 }. It has a total absorption of 100m^{2}sabine. If the hall is filled with audience who add another 80m^{2}sabine, then find the difference in reverberation time.
22. What is NDT? and how ultrasonic wave used for NDT?

23. What is the difference between spontaneous emission and stimulated emission?

24. What is LED? Give its working principle?

**PART C**

**Answer any 3 Questions each carries 6 marks.**
25. Considering the transverse vibration in a stretched string, derive the differential equation of one dimensional wave.

26. Light from a monochromatic source is allowed to fall on a single slit. Two lenses are given. With the help of neat diagram write the experimental set up for obtaining the diffraction pattern. Deduce the condition for getting bright and dark regions on the screen. Also obtain the width of central maximum.

27. How a Nicol prism can be constructed from a calcite crystal? How can be it be used as polarizer and as a analyzer?

28. Formulate a Schrodinger’s time dependent equation starting from a plane wave equation by using a de Broglie’s formula and Einstein’s relation for photon Energy.

**PART D**

**Answer any 3 Questions. Each Question carries 6 marks**
29. With a neat diagram explain how ultrasonic waves are produced by piezoelectric oscillator.

30. What are the factors affecting acoustics of a building?

31. Outline the principle and working of Ruby Laser.

32. Define numerical aperture of an optical fiber and derive an expression for NA of step index fibre.

**KTU Previous Question Paper 2016 with answers for Engineering Physics**

**ANSWERS**

**1. What do you mean by quality factor of an oscillator?**

**ANS:**

Quality factor

**(Q)**of an oscillator is defined as 2Π times the ratio of energy stored to the average energy loss per period.**2.What is the relation between path difference and phase difference in wave motion?**

**ANS:**

A path difference of x

_{0}will correspond to a phase difference of**3.Two independent source of light can not produce interference fringes. Why?**

**ANS:**

Two sources of light with same wavelength and amplitude with a constant phase difference is called coherent sources.

Only coherent sources can produce interference pattern. Two independent sources can never be mutually coherent.

**4.Define dispersive power of a grating.**

**ANS:**

Dispersive power of grating is defined by the ratio of change in angle of diffraction to corresponding change in wave length. Dispersive power of grating is given by

**5.Distinguish between plane polarized light and unpolarized light.**

**ANS:**

• Un-polarized light has electrical component in every direction, at any given time, but the polarized light has the electric component only in one direction for a given time.

• When the un-polarized light is polarized, it is always reduced in intensity.

**6.What is Meissner effect ?**

**Ans:**

When a superconductor is placed in a magnetic field, that superconductor expels magnetic flux completely, a property of superconductors which has come to be known as Meissner effect.

**7.What is phase space?**

**ANS:**

Phase-space is such a space, a point in which represents a micro-state of the system. The 2f-dimensional space with f generalized position co-ordinates and f generalized momenta is called a phase space.

**8.What is the probability interpretation of wave function?**

**ANS:**

If a particle exists in a given region of space, the total probability of finding the particle in that region is one. Mathematically,

**∫Ψ*Ψdτ=1**

where dτ is the volume element

Ψ*Ψ represents probability density

**9.What is the relation connecting reverberation time and total absorption?**

**ANS:**

**Reverberation Time**is the time it takes the sound to decay away 60 dBs.

__Sabine’s formula__

T = 0.16 V / A

where V is the room volume in cubic meters, and A is the total absorption in square meters.

**10.What is magnetostriction effect?**

**ANS:**

Magnetostriction effect is the property of a ferromagnetic materials (iron, nickel) that causes them to change their shape and dimensions when they are kept in a magnetic field.

**11.Write any two advantage of Hologram over photographic images.**

**ANS:**

In hologram we have the freedom of vision to change the view point and the focus, while we see a three dimensional object i.e. we have a 3D view ( Stereoscopic vision). A hologram records both intensity and phase variations.

A photograph is a two dimensional version of a 3D object i.e. it is a still of a 3D scene, with fixed viewpoint and focus. Thus there is no stereoscopic vision. A photographic plate is sensitive to only the intensity variation and not the phase variations.

**12.Distinguish between step index fiber and Graded index fiber.**

**ANS:**

**PART B**

*Answer any 10 questions. Each question carries 4 marks***13.Compare an electrical and mechanical oscillator.**

**ANS:**

**Electrical oscillator**

An oscillator can be defined as an electronic circuit which converts dc power from the supply to ac power in the load. It is circuit which generates an output signal without any external input signal.

**Mechanical Oscillator**

In mechanical oscillator there is only a transformation from K.E to P.E and vice versa. Total Energy of a harmonic oscillator with no dissipative forces remains constant.

**14. A transverse wave on a stretched string is described by y(x,t)=4.0sin(25t+0.016x+π/3) where x and y are in cm and t is in second.**

**Obtain the (i) Speed (ii) Amplitude (iii) Frequency and(iv)Initial phase at the origin.**

**ANS:**

**(i)**Instantaneous velocity is,

**(ii)**amplitude is 4

**(iii)**Frequency,

**ω=2πf**

**f=ω/2π**

where,

**ω=25;****f=25/2π;**

**=3.98Hz**

**(iv)**Initial phase at origin is,

**π/3**

**15. With Newton’s rings arrangement, nth dark ring formed by light of wavelength 6000 A° coincides with the (n+1)th dark ring for light of wavelength**.

*4500A°.*If the radius of curvature of the convex surface is 90 cm, find the diameter of the nth ring for light wavelength 6000 A°**ANS:**

We know that,

for dark ring

**2t=nλ**; n

^{th}dark ring of first wave coincide with (n+1)

^{th}dark ring;

So,

**nλ**_{1}=(n+1)λ_{2}**n**x

**6000=(n+1)**x

**4500**by solving we get,

**n=3**

We know that,

**r**

_{n}^{2}=Rnλ**r**

_{n=√Rnλ}
r=√(90×10

^{-2}x3x6000x10^{-10})
r=1.272mm.

**16. A plane transmission grating has 6000 lines/cm. Find the angular separation between two wavelengths 500nm and 510nm in the 3**

^{rd}order.**ANS:**

We know that;

SinΘ=Nnλ

N be the number of lines in one metre of the grating

Θ

_{1}=Sin^{-1}(6000x100x3x500x10^{-9})
Θ

_{1}=64.16^{o}
Θ

_{2}=Sin^{-1}(6000x100x3x510x10^{-9})
Θ

_{2}=66.64^{o}
angular separation=

**Θ**_{2 }– Θ_{1}**=2.48**

^{o}**17. The refractive index of a calcite is 1.658 for ordinary ray and it is 1.486 for extraordinary ray. A slice having thickness 0.9×10**

^{-4}cm is cut from the crystal. For what wavelength the slice will acts as a (i) Quarter wave plate. (ii) Half wave plate.**ANS:**

**(i)**For Quarter Wave Plate, thickness

**(ii)**For Half wave plate, thickness

**18. Distinguish between Type I and Type II superconductors with examples.**

**ANS:**

Type I Superconductors | Type II Superconductors |

1. Soft superconductors are those which can tolerate impurities without affecting the superconducting properties. | 1. Hard superconductors are those which cannot tolerate impurities, i.e., the impurity affects the superconducting property. |

2. They have low critical field. | 2. They have high critical field. |

3. Show complete Meissner effect. | 3. Hard super conductors trap magnetic flux and hence Meissner effect is not complete. |

4. The current flows through the surface only. | 4. It is found that current flows throughout the material. |

5. Eg. Tin, Aluminum | 5. Eg. Tantalum, Neobium |

**19. Calculate the De Broglie wavelength of electron whose kinetic energy is 10Kev.**

**ANS:**

Kinetic Energy

**KE=1/2(mv**^{2})**λ=h/p**

**2Em=P**

^{2}
P=√(2Em)

λ=h/√(2Em)

1eV=1.6×10

^{-19}J ; mass of e=9.1×10^{-31}kg ; h=6.626×10^{-34}m^{2}kg/s
Substituting the value we get,

λ=1.22nm.

**20. Distinguish between Macrostate and Microstate of a system.**

**ANS:**

**Macrostate and Microstate**

The state of a physical system characterized by its bulk parameters like pressure, volume, temperature, mass etc. is called

**Macro states.**
A

**Microstate**of a system is characterized by the value of coordinates of position and momentum for all particle on a system at any instant.
Microstate changes with time without affecting the Macrostates. Thus an enormously large number of microstates correspond to each macrostate of the system.

**21. The volume of a hall is 3000 m**

^{3 }. It has a total absorption of 100m^{2}sabine. If the hall is filled with audience who add another 80m^{2}sabine, then find the difference in reverberation time.**ANS:**

We know Sabine’s formula;

T = 0.16 V / A

Here,

V- volume

A- area of absorption

reverberation time T

_{1}= 0.16×3000/100**=4.8 Sec**

T

_{2}=0.16×3000/180**=2.67 Sec**

difference in reverberation time,

**T**

_{2}– T_{1}**=2.13 Sec**

**22. What is NDT? and how ultrasonic wave used for NDT?**

**ANS:**

Nondestructive testing is a method of finding defects in an object without harming the object. NDT is used to look for internal changes or signs of wear on airplanes. Discovering defects will increase the safety of the passengers. The railroad industry also uses nondestructive testing to examine railway rails for signs of damage. Sound with high frequencies, or

**ultrasound**, is one method used in NDT. Basically, ultrasonic waves are emitted from a transducer into an object and the returning waves are analyzed. If an impurity or a crack is present, the sound will bounce off of them and be seen in the returned signal. In order to create ultrasonic waves, a transducer contains a thin disk made of a crystalline material with piezoelectric properties, such as quartz. When electricity is applied to piezoelectric materials, they begin to vibrate, using the electrical energy to create movement. Remember that waves travel in every direction from the source. To keep the waves from going backwards into the transducer and interfering with its reception of returning waves, an absorptive material is layered behind the crystal. Thus, the ultrasound waves only travel outward.**23. What is the difference between spontaneous emission and stimulated emission?**

**ANS:**

**spontaneous emission**

The emission of photons by the natural de-excitation transition of atoms, molecules, ions etc. is known as spontaneous emission process. This is an uncontrolled and natural phenomenon in which each excited atom emit photons independently in random direction, phase and polarization.

**stimulated emission**

The process of de-excitation transition with the emission of radiation on finding an identical radiation as stimuli to trigger the emission process and is known stimulated emission.

**24. What is LED? Give its working principle?**

**ANS:**

LED operating on the principle of injection of luminescence. Basically LED is a semiconductor pn junction device capable of emission of electromagnetic radiation under forward-biased condition. LED emits light under forward biased condition. When the external voltage exceeds the barrier potential, recombination between electrons and holes take place. The minority carrier concentration on both sides of the junction are considerably increased under this condition, which increases their rate of recombination. Thus electromagnetic radiation emitted.

**PART C**

**Answer any 3 Questions each carries 6 marks.****25. Considering the transverse vibration in a stretched string, derive the differential equation of one dimensional wave.**

**ANS:**

**Ans:**

When a string stretched btween A and B is plucked, let tension acts at P&Q which are a

**26. Light from a monochromatic source is allowed to fall on a single slit. Two lenses are given. With the help of neat diagram write the experimental set up for obtaining the diffraction pattern. Deduce the condition for getting bright and dark regions on the screen. Also obtain the width of central maximum.**

**ANS:**

**Fraunhofer Diffraction**

The source and screen are moved to large distance from the diffracting aperture. This limiting case is called Fraunhofer diffraction. Fraunhofer conditions can be established in the laboratory by using two converging lenses.

The first lens converts the diverging wave from the source into a plane wave. The second lens converges the waves leaving the aperture to a point P.

Consider a narrow slit AB of width ‘a’ on which monochromatic light of wavelength ‘λ’ is falling from a collimating lens L. The wavefront incident on the slit AB is plane. Let the light emerging from AB be incident on another lens L’.

The path difference between wavelets from A and B is AL=AB SinΘ=a SinΘ, where ‘a’ is the width of the slit and Θ is the angle which the diffracted beam makes with the direction OP.

If the path difference between wavelets from A and B is λ, i.e, a SinΘ=λ

Path difference between wavelets from A and those from O is λ/2 and they cancel one another. All other pairs of corresponding points in the two halves OA and OB of the wavefront will also differ by a path by λ/2 and cancel each other. Thus dark band will appear at P’

First minimum, on either side of C will appear in a direction Θ

SinΘ=λ/a

direction of the n

^{th}minimum is given by
SinΘ

_{n}=nλ/a, where n=1,2,3,………etc
Lens L’ has the screen at its focus,

sinΘ=λ/a=x/f

x=fλ/a

x is the distance of the first minimum from C and f is the focal length of lens L’

Hence width of central maximum,

2x=2fλ/a

If AN= 3λ/2

i.e. if a sinΘ’=3λ/2

The direction of the nth secondary maximum is given by

sinΘ’

_{n}=(2n+1)λ/2a
where n=1,2,3,…etc.

**27. How a Nicol prism can be constructed from a calcite crystal? How can be it be used as polarizer and as a analyzer?**

**ANS:**

Nicol prism is an optical device made from calcite crystal. This is used in many optical instruments for producing and analyzing polarized light. It removes one of the two refracted rays, usually the O-ray, by total internal reflection.The transmitted E-ray is plane polarized. It is constructed from a calcite crystal whose length is about three times its width.The ends are cut down from 71

^{o }in the principal section to a more acute angle of 68^{o}. The crystal is then cut into two pieces diagonally through one of the obtuse corners. The two cut surfaces are polished optically flat and then cemented together in their original position with a transparent cement called canada balsam. Canada balsam is used because its refractive index lies between the refractive indices of calicite for the O and E rays.
Optically the balsam is denser than the calicite for the E-ray and less dense for the O-ray. The E-ray, therefore, will be refracted into the balsam and on through the calcite crystal, whereas the O-ray, for large angles of incidence, will be totally reflected.

Nicol prism can be used as a polarizer and an analyser. It is used in specially constructed microscopes for studying the optical properties of crystals.

**28. Formulate a Schrodinger’s time dependent equation starting from a plane wave equation by using a de Broglie’s formula and Einstein’s relation for photon Energy.**

**ANS:**

The differential equation for a wave associated with a particle and propagating along X- direction may be written as

**PART D**

**Answer any 3 Questions. Each Question carries 6 marks****29. With a neat diagram explain how ultrasonic waves are produced by piezoelectric oscillator.**

**ANS:**

**Principle: Inverse piezo electric effect**

• If mechanical pressure is applied to one pair of opposite faces of certain crystals like quartz, equal and opposite electrical charges appear across its other faces. This effect is called as piezo-electric effect.

• The converse of piezo electric effect is also true.

• If an electric field is applied to one pair of faces, the corresponding changes in the dimensions of the other pair of faces of the crystal are produced. This effect is known as inverse piezo electric effect.

Construction The circuit diagram is shown in Figure

• The quartz crystal is placed between two metal plates A and B.

• The plates are connected to the primary (L3) of a transformer which is inductively coupled to the electronics oscillator.

• The electronic oscillator circuit is a base tuned oscillator circuit.

• The coils L1 and L2 of oscillator circuit are taken from the secondary of a transformer T.

• The collector coil L2 is inductively coupled to base coil L1.

• The coil L1 and variable capacitor C1 form the tank circuit of the oscillator. Working

• When H.T. battery is switched on, the oscillator produces high frequency alternating voltages with a frequency.

• Due to the transformer action, an oscillatory e.m.f. is induced in the coil L3. This high frequency alternating voltages are fed on the plates A and B.

• Inverse Piezo-electric effect takes place and the crystal contracts and expands alternatively. The crystal is set into mechanical vibrations.

• The frequency of the vibration is given by

where P = 1,2,3,4 … etc. for fundamental, first over tone, second over tone etc., Y = Young’s modulus of the crystal and ρ = density of the crystal.

• The variable condenser C1 is adjusted such that the frequency of the applied AC voltage is equal to the natural frequency of the quartz crystal, and thus resonance takes place.

• The vibrating crystal produces longitudinal ultrasonic waves of large amplitude.

**30. What are the factors affecting acoustics of a building?**

**ANS:**

**(1) Reverberation:**Reverberation is a desirable property of auditoriums to the extent that it helps to overcome the inverse square law drop off of sound intensity in the enclosure. However, if it is excessive, it makes the sounds run together with loss of articulation – the sound becomes muddy, garbled.

**(2) Loudness:**

(3) Focusing

(4) Echoes

(5) Echelon effect

**(6) Resonance:**the frequencies of forced vibrations may be the same thus resulting in the resonance. Some times even though the frequency of crated sound is not equal to that of the original sound, they will super pose with each other. Due to their interference the original sound is distorted.

**(7) Noise:**Generally there are three types of noises. They are (i) Air-borne noise (ii) Structure borne noise (iii) Inside noise. The prevention of noise is known as sound insulation or soundproofing. The method of sound insulation depends on the type of noise to be decreased.

**31. Outline the principle and working of Ruby Laser.**

**ANS:**

**32. Define numerical aperture of an optical fiber and derive an expression for NA of step index fibre.**

**ANS:**

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