Time: 2 hours

Maximum marks: 50

Notes :

i) Neat diagrams must be drawn wherever necessary.

ii) Figures to the right indicate full marks.

iii) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed.

iv) Assume suitable data, if necessary.

v) All questions are compulsory.

Physical constants :

1. Mass of electron = m_{e} = 9.1×10^{-31} kg

2. Charge of electron = e= 1.602×10^{-19} C

3. Planck’s constant = h = 6.63×10^{-34}J.s.

4. Velocity of light = C= 3×10^{8} m/sec

5. Avogadro’s number = 6.023 x 10^{23} gms/mole

1. (a) Derive expression for path difference in reflected light and derive the conditions for constructive and destructive interference for a film of uniform thickness. [6M]

(b) Explain any one application of ultrasonic waves. [3M]

(c) The average reverberation time of a hall is 1.5 sec and the area of the interior surface is 3340 m^{2}. If the volume of the hall is 13000 m^{3}, find the absorption coefficient. [3M]

**OR**

2. (a) Explain magneto-striction effect. Explain how magneto-striction oscillator is used to produce ultrasonic waves with the help of neat circuit diagram. [6M]

(b) Explain an application of interference Antireflection coating. [3M]

(c) A plane transmission grating has 5000 lines/cm. Find out the highest order spectrum observed if incident light has λ = 6000 Å. [3M]

3. (a) What is Double refraction ? Explain Huygens’s theory of double refraction. [6M]

(b) What is Holography ? Explain the process of hologram recording. [3M]

(c) Calculate the mobility of charge carriers in doped silicon whose conductivity is 100/Ω-m and the Hall coefficient is 3.6 x 10^{-4}m^{3}/C. [3M]

**OR**

4. (a) Derive an expression for conductivity in intrinsic and extrinsic Semiconductors. [6M]

(b) Define the following : [3M]

i) Stimulated Emission

ii) Meta-stable state

iii) Pumping.

(c) Plane polarized light passes through a positive double refracting crystal of thickness 40 μm and emerges out as circularly polarized light. If the birefringence of the crystal is 4 x 10^{-5}, find the wavelength of the incident light. [3M]

5. (a) Derive an expression for energy of a particle trapped in an infinite potential well. [6M]

(b) Define phase velocity and group velocity. Derive the relation between them. [4M]

(c) An electron beam is accelerated from rest through a potential difference of 200 V. Calculate the associated wavelength. [3M]

**OR**

6. (a) What is De-Broglie’s hypothesis of matter waves. Show that the De-Broglie’s wavelength of a charged particle is inversely proportional to the square root of the accelerating potential. [6M]

(b) Write down the conditions which are to be satisfied by well behaved wave function. [4M]

(c) Calculate the energy required to excite the electron from its ground state to fourth excited state in a rigid box of length 0.1 nm. [3M]

7 . (a) What is superconductivity ? Explain the Meissner effect in superconductors. [6M]

(b) Explain the following properties of Nano-particles : [4M]

i) Magnetic property

ii) Mechanical property.

(c) Explain the applications of nano particles in medical and automobile field. [3M]

**OR**

8. (a) Explain the synthesis of Nano particles by using mechanical method. [6M]

(b) Explain zero electrical resistance property and isotope effect in superconductor. [4M]

(c) Explain any one application of superconductors in brief. [3M]

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