Download Derive an expression for time dilation and give an

JRE Group of Institutions, Greater Noida
Modal Paper
Physics
2012-13
Unit-I
1. Derive an expression for time dilation and give an example to show that time dilation
is a real effect.
2. Show that x2 + y2 + z2 – c2t2 is invariant under Lorentz transformation.
3. State Einstein’s postulates of special theory of relativity. Derive inverse Lorentz
transformation equations.
4. Show that x2 + y2 + z2 – c2t2 is invariant under Lorentz transformation.
5. 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’?
6. An airfoce rocket is chasing enemy’s spaceship. From earth, it is found that the speed
of rocket is 2.55 X 1010 cm s-1 while that of enemy’s ship is 2.25 X 1010 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
7. Deduce an expression for the variation of mass with velocity.
8. 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.
9. Differentiate inertial and non-inertial frames and show that inertial frames move with
constant velocity relative to each other.
10. The mass of a moving electron is 11 times its rest mass. Find its kinetic energy and
momentum.
11. Show that the momentum of a particle of rest mass m0 and kinetic energy KE is given
by the expression:
P = √(K2E/ c2 + 2m0 KE)
Unit-II
1. Deduce the equation for the propagation of plane electromagnetic wave in free space.
Show that electric and magnetic vectors are normal to each other and to the direction
of propagation of the wave.
2. Write the Maxwell’s equation. Explain the physical significance of each equation.
3. Prove that the velocity of plane EM – wave in the vacuum is given by
C = 1/√μ0ε0
4. Deduce Maxwell’s equation for free space and prove that em-wave is transverse
5. Deduce pointing theorem for the flow of energy in an electromagnetic field. Give the
physical significance of each term.
6. 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.
7. Explain the concept of displacement current and show how it led to the modification
of Ampere’s law.
8. Show that the ware equation for electric field E is given by
▼2 E = μ0ε0 (∂2E/∂t2)
9. Derive electromagnetic wave equation in conducting medium and discuss its solutions.
10. If the earth receives 2 cal min-1cm-2 solar energy, what are the amplitudes of electrics
and magnetic field of radiation?
11. Assuming that all energy from a 1000 Watt lamp is radiated uniformly, calculate the
average value of the intensities of electric and magnetic field of radiation at a distance of
2 m from the lamp.
Unit-3
12. State and discuss the basic condition for observing the phenomena of interference of
Light.
13. 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?
14. What are missing orders? What particular spectra would be absent if the width of
transparencies and opacities of the grating are equal?
15. 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.
16. Derive an expression for the path difference produced by a thin wedge - shaped film ,
in case of reflected and transmitted light.
17. Describe the features of a double slit Fraunhofer diffraction. What is the effect of (a)
increasing the slit width, (b) increasing the slit sepration and (c) increasing the
wavelength of light?
18. Newton’s rings are formed in reflected light of wavelength 6000Å with a liquid
between the plane and curved surfaces. If the diameter of 6th 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.
19. Discuss the phenomena of Fraunhofer diffraction at a single slit and show that the
relative intensities of the successive maxima are given as
1:4/9π2:4/25π2 : 4/9π2:-------------20. Define the limit of resolution and Resolving power of an optical apparatus. Derive an.
expression for the Resolving power of a diffraction grating.
21. 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 of the slit.
22. 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.
23. 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 300. Calculate the wavelengths of light used.
24. Find the possible maximum number of orders with a grating and discuss the cases.
Unit-4
25. 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.
26. Describe half shade polarimeter. find specific rotation of a lane sugar solution if the
plane of polarization is turned by 26. 4˚. Length of tube is 20cm and concentration of
sugar is 20℅.
27. Obtain expression for minimum thickness of a quarter wave plate .Find thickness of a
quarter ware plate for λ = 589 nm μ0 = 1۠55; μe = 1.54.
28. Explain phenomenon of double refraction. Descibe Huygen’s theory of double
refraction when optic axis is parallel to upper face and lying in plane of incidence.
29. Describe the construction of a nicol prism and show that it can use as a polarizer or as
an analyzer.
30.80 gm of impure sugar is dissolved in a litre of water. The solution gives an optical
rotation of 9.90 when placed in a tube of length 20 cm. If the specific rotation of pure
sugar is 660 dm-1(gm/cc)-1, calculate the percentage purity of the sugar sample.
31.Write short notes on
(i) Spontaneous absorption
(ii) Stimulated emission
(iii) Spontaneous absorption
(iv) Optical pumping
(v) Population inversion
(vi) Resonant cavity
32. What are Einstein’s coefficients? Derive Einstein relation.
33. Describe the construction and action of the ruby laser.
34. Explain the action of a helium-neon laser. How is it superior to a ruby laser?
35. Explain the principle of optical pumping and stimulated emission of radiation.
Discuss the properties of laser radiation and mention some of its applications.
36. A certain ruby laser emits 1.00 J pulses of light whose wavelength is 694nm. What is
the minimum number of Cr3 + ions in the ruby crystal?
37. 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 Å. Find the
energy of one emitted photon and the total energy available per laser pulse.
38. Give the working and construction of semiconductor laser. How we can create
population inversion in diode laser.
Unit-5
39. Explain basic principle of optical fibre. Discuss fibre classification.
40. Explain acceptance angle and acceptance cone of a fibre. What do you mean by
numerical aperture of a fibre? Derive expression for them.
41. Explain single mode and multimode fibre. What are advantages of optical fibre over
copper wire?
42. Discuss the phenomenon of dispersion in optical fibre.
43. Explain the difference between step index and graded index fibre.
44. What are signal losses or attenuation mechanism in a fibre.
45. Discuss the different type of losses in optical fibre.
46. What is holography? Discuss the construction and reconstruction of image on a
hologram.
47. Calculate the numerical aperture, acceptance angle and the critical angle of the fibre
from the following: n1=1.5(ref. index of core) and n2 = 1.45(ref. index of cladding)
48. A glass clad fibre is made with core glass of refractive index 1.5 and the cladding is
doped to give a index difference of 0.0005. Determine (a) the cladding refractive index,
(b) the critical reflection angle, (c) the critical acceptance angle and (d) the numerical
aperture.
49.A multimode fibre has a core diameter of 70 μm and the relative refractive index
difference of 1.5%. It operates at the wavelength of 0.85μm. The refractive index of the
fibre is 1.46. Calculate:
(a) The refractive index of the cladding
(b) The normalized frequency V-number of the fibre
(c) The total number of guided modes in the fibre.
50. The core and cladding refractive indices of a step index fibre are 1.6 and 1.44 μm
respectively. An electromagnetic wave having wavelength of 0.8μm is propagating
through the fibre in guided mode through the core of the fibre. Find out maximum and
minimum value of phase constant.
Sol. 50.
The max value of phase constant = (2π/λ)n1
The min value of phase constant = (2π/λ)n2