JRE Group of Institutions ASSIGNMENT # 1 Special Theory of Relativity

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1 ASSIGNMENT # 1 Special Theory of Relativity 1. What was the objective of conducting the Michelson-Morley experiment? Describe the experiment. How is the negative result of the experiment interpreted? 2. State Eintein s postulates of special theory of relativity. Explain why galilean relativity failed to explain the actual results of Michelson Morley experiment. 3. Derive an expression for time dilation and give an example to show that time dilation is a real effect. 4. Show that the circle x 2 + y 2 = a 2 in frame S appears to be an ellipse in a frame S which is moving with velocity v relative to s. 5. Show that x 2 + y 2 + z 2 c 2 t 2 is invariant under Lorentz transformation. 6. If at the time t = t = 0, the origin of the systems s and S just coincide and a spherical pulse of light is produced at the common origin, show that the speed of propagation of the spherical wavefront is the same in both systems i.e c, where S is moving relative to stationary system S. 7. Deduce the relativistic velocity addition theorem. Show that it is consistent with Einstein s second Postulate. 8. Verify the statement that no material particle can attain speed of light c. 9. Calculate the length of a rod of length 5m in a frame of reference which is moving with a velocity 0.6 c in a direction making an angle of 30 with the rod. 10. With what velocity should a spaceship fly so that every day on it may correspond to three days on the earth s surface?

2 ASSIGNMENT # 2 Special theory of relativity 1. Establish Einstein s mass energy relation. Show that if the variation of mass with the velocity is taken into account, the kinetic energy of the particle of rest mass m o and moving with velocity v is given by k = m o c 2 [ ( 1- v 2 /c 2 ) -1/2-1] 2. Find the kinetic energy and momentum of an electron moving with speed 0.6 c. 3. What is the length of a meter-stick appear to an observer at rest when it moves parallel to its length and its mass is measured as 3/2 times that of its rest mass? 4. An experimenter observes a radioactive atom moving with a velocity of 0.25c. The atom then emits a beta particle, which has a velocity of 0.9c, relative to the atom in the direction of its motion. What is the velocity of the beta particle as observed by the experimenter? 5. A man leaves the earth in a rocket that makes a round trip to the nearest star which is 4 light years away from Earth, at a speed of 0.8c in the direction of the star. How much younger will he be, w.r.t. to an observer on Earth, on his return than his twin brother who preferred to stay back? 6. Get an expression for Einstein s mass-energy relationship. How will this expression get modified when the speed of the particle v is very small in comparison to the speed of light c? 7. The total energy of a moving meson is exactly twice its rest energy. Find the speed of the meson. 8. Show that E 2 /c 2 P 2 is invariant under Lorentz transformation. 9. An airfoce rocket is chasing enemy s spaceship. From earth, it is found that the speed of rocket is 2.55 X cm s -1 while that of enemy s ship is 2.25 X cm s -1. What is the relative velocity of: (i) enemy s ship as seen by air force rocket. (ii) air force rocket as seen by enemy s ship. (iii) air force rocket with respect to enemy s ship as seen from earth. (iv) enemy s ship with respect to air force rocket as seen from earth. 10. Deduce an expression for the variation of mass with velocity.

3 ASSIGNMENT # 3 Interference 1. Define coherent sources. Discuss why two independent sources of light of same wavelength can not show interference. 2. State and discuss the basic condition for observing the phenomena of interference of Light. 3. How does the interference pattern by reflection in thin films differ from that of refraction? Why? 4. Explain why a thin transparent film appears coloured when observed in reflected light. Why an extended source is required for observing the bands? Why are the colours not observed in case of thick film? 5. A soap film of μ = 1.33 is illuminated by white light incident at an angle of 45. The light refracted by it is examined by a spectrometer and a bright band is found corresponding to a wavelength 6000Å. Find the thickness of the film. 6. Describe and explain the formation of Newton s tings in reflected monochromatic light. Why Newton s rings are circular? 7. Newton s rings are formed in reflected light of wavelength 6000Å with a liquid between the plane and curved surfaces. If the diameter of 6 th bright ring be 3.1 mm and the radius of curvature of the curved surfaces is 100 cm. Calculate the refractive index of the liquid. 8. Derive an expression for wavelength of light in Newton s ring experiment for transmitted light if the plane glass plate is replaced by an another convex lens in such a way that both lenses are in contact with their curved surfaces. 9. Derive an expression for the path difference produced by a thin wedge - shaped film, in case of reflected and transmitted light. 10. Describe the principle and method of production of interference filter. 11. A glass microscope lens of refractive index is coated with magnesium fluoride (μ = 1.38) film to increase the transmission of normally incident yellow light (λ = 5800Å). What minimum thickness should be deposited on the lens? 12. Write a note of anti-reflection coating.

4 ASSIGNMENT # 4 Diffraction 1. Determine the width of the m th order maxima for the n- slit Fraunhofer s diffraction pattern. 2. Give the theory of formation of diffraction patterns using a plane transmission grating. How would your use it to determine the wavelength of light. 3. Get the expression of and distinguish between dispersive power and resolving power of transmission grating. 4. Discuss the phenomena of Fraunhofer diffraction at a single slit and show that the relative intensities of the successive maxima are given as 1:4/9π 2 :4/25π 2 : 4/9π 2 : Define the limit of resolution and Resolving power of an optical apparatus. Derive an. expression for the Resolving power of a telescope and a microscope. 6. A parallel beam of mono-chromatic light is allowed to be incident on a plane grating having 500 lines/ cm and the second order spectral line is found to be diffracted through Calculate the wavelengths of light used. 7. Light of wavelength 5000 Å is incident normally on a slit. The first minimum of diffraction pattern is observed to lie at a distance of 5 mm from the central maximum on a screen placed at a distance of 2 m from the slit. Calculate the width the width of the slit. 8. A microscope objective gathers light over a cone of semi-angle 30 and uses visible light (λ = 5500Ǻ).Estimate its resolving limit. 9. Find the minimum number of lines that a diffraction grating would need to have in order to resolve in first order the red doublet given by a mixture of hydrogen and deuterium. The wavelength difference is 1.8 Ǻ at λ =6553 Å. 10. A diffraction grating is just able to resolve two lines of wavelength Ǻ and Å in the first order.will it resolve the lines Ǻ and Å in the Second order. 11. A telescope of a certain objective has diameter of 100 inches.estimate the smallest angle between two stars that can be separated by it. 12. In a grating spectrum, which spectral line in 4 th order will overlap with 3 rd order line of 5461 Å?

5 ASSIGNMENT # 5 Polarization 1. Define double refraction, Describe construction and working with use of a Nicole prism. 2. Describe half shade polarimeter find specific rotation of a lane sugar solution if the plane of polarization is turned by Length of tube is 20cm and concentration of sugar is Discuses Huygens s explanation of double refraction.give the construction and theory of half wave plate. 4. How would you produce and detect the following with the help of a nicol prism and a quarter wave plate. (1) Plane polarized light (ii) circularly polarized light (iii) elliptically polarized light. 5. Explain Brewster s law. Show that when light is incident on a transparent medium at polarizing angle, the reflected and refracted rays are at right angles. 6. Obtain expression for minimum thickness of a quarter wave plate.find thickness of a quarter ware plate for λ = 589 nm μ 0 = 1 55; μe = A tube 20 cm long with a solution of 15 gm of cane sugar in 100cc, of water is placed in the path of polarized light. Find the angle of rotation of plane of polarization if the specific rotation of cane sugar is A 20 cm long tube containing sugar solution rotates the plane of polarization by If the specific rotation is 66 0, calculate the strength of the solution gm of impure sugar is dissolved in a litre of water. The solution gives an optical rotation of when placed in a tube of length 20 cm. If the specific rotation of pure sugar is 66 0 dm -1 (gm/cc) -1, calculate the percentage purity of the sugar sample.

6 1. Write short notes on JRE Group of Institutions ASSIGNMENT # 6 LASER (i) Spontaneous absorption (ii) Stimulated emission (iii) Spontaneous absorption (iv) Optical pumping (v) Population inversion (vi) Resonant cavity 2. What are Einstein s coefficients? Derive Einstein relation. 3. Describe the construction and action of the ruby laser. 4. Explain the action of a helium-neon laser. How is it superior to a ruby laser? 5. Explain the principle of optical pumping and stimulated emission of radiation. Discuss the properties of laser radiation and mention some of its applications. 6. What are differences between spontaneous and stimulated emission. 7. Why is spontaneous radiation incoherent? 8. A certain ruby laser emits 1.00 J pulses of light whose wavelength is 694nm. What is the minimum number of Cr 3 + ions in the ruby crystal? 9. A pulsed laser is constructed with ruby crystal as active element. Ruby rod contains typically a total of 3X10^19 Cr3+ ions.if the laser emits light at 6943 A o find the energy of one emitted photon and the total energy available per laser pulse.

7 ASSIGNMENT # 7 Electrostatic 1. Write the Maxwell s equation. Explain the physics significance of each equation. 2. Prove that the velocity of plane EH wave in the vacuum is given by C = 1/ μ 0 ε 0 3. Deduce pointing theorem for the flow of energy in an electromagnetic field. 4. Show that the ware equation for electric field E is given by 2 E = μ 0 ε 0 ( 2 E/ t 2 ) 5. Deduce Maxwell s equation for free space and prove that em-wave is transverse. 6. Show that equation of continuity divj + ρ/ t = 0 is contained in Maxwell s equations. 7. It the earth receives 2 cal min -1 cm -2 solar energy, what is the amplitude of electric and magnetic fields of radiation? 8. Assuming that all the energy from a 1000 watt lamp is radiated uniformly; calculate the average intensities of electric and magnetic fields of radiation at a distance of 2 m from lamp. 9. State and explain Ampere s circuital law. Use it to find the magnetic filed induction B at a point within a current carrying (i) long solenoid (ii) tortoid. 10. Explain the concept of displacement current and show how it led to the modification of Ampere s law.

B.Tech. First Semester Examination Physics-1 (PHY-101F)

B.Tech. First Semester Examination Physics-1 (PHY-101F) Note : Attempt FIVE questions in all taking least two questions from each Part. All questions carry equal marks Part-A Q. 1. (a) What are Newton's