# ENGINEERING PHYSICS KTU 2016 PREVIOUS QUESTION PAPER WITH ANSWERS FOR S1,S2 FIRST YEAR STUDENTS

**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 nth minimum is given by

SinΘn=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 71o in the principal section to a more acute angle of 68o. 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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