IGNOU PHE-09 Optics - Latest Solved Assignment

1. a) Describe polarisation of light by reflection. How does degree of polarisation vary with angle of incidence of light?
b) The sodium lamp used in a physics laboratory gives out light uniformly. Suppose that the lamp uses 60 W. Calculate the magnitude of electric field.
c) Discuss the concept of missing orders with reference to double slit diffraction pattern.
d) Discuss spatial evolution of Fresnel diffraction pattern.

2. a) Obtain expressions for reflection and transmission amplitude coefficients when electric vector associated with a plane monochromatic electromagnetic wave is in the plane of incidence.
b) Obtain an expression for elliptically polarised light resulting due to superposition of two orthogonal linearly polarised light waves. Show that plane polarised light and circularly polarised light are special cases of elliptically polarised light.

3. a) Obtain the expression for shift in fringes when a thin transparent sheet is introduced in the path of one of the waves in a double slit interference experiment
b) A plano-convex lens of radius 1.0 m is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the 10th and 5th dark rings in the reflected light are 4.50 × 10-3m and 3.36 × 10-3m. Next, the space between the lens and the glass plate is filled with a liquid. The diameter of the 5th ring changes to 3.0×10-3m. Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is 589 nm.

4. a) A plane light wave of wavelength 580 nm falls on a long narrow slit of width 0.5 mm. (i) Calculate the angles of diffraction for the first two minima. (ii) How are these angles influenced if the width of slit is changed to 0.2 mm? (iii) If a convex lens of focal length 0.15 m is now placed after the slit, calculate the separation between the second minima on either side of the central maximum.
b) Discuss Rayleigh’s criterion for resolving power of an optical instrument. Obtain an expression for resolving power of a microscope.

5. a) An atomic system consisting of two energy levels, with population of higher energy level less than that of the lower level, is in thermal equilibrium. Show that the absorption of radiation dominates stimulated emission if radiation of appropriate frequency is introduced into the system. Comment on the consequences of this fact for laser action.
b) Two energy levels of an atomic system are separated by energy corresponding to frequency 3.0 × 1014 Hz. Assuming that all atoms are in one or the other of these two energy levels, compute the fraction of atoms in the upper energy level at temperature 400 K. Take kB = 1.38×10-23JK-1 and h = 6.6×10-34Js.
c) The refractive indices of the core and cladding materials of an optical fibre are 1.51 and 1.39 respectively. Calculate the numerical aperture and light gathering capacity of the fibre.

1. Answer any four parts:
a) Write down Maxwell’s field equations for free space and obtain expressions for velocity of electromagnetic waves.
b) Discuss the significance of accommodation and convergence of human eye in respect of perception of light.
c) Discuss, with necessary theory, how is interference pattern in Young’s double slit experiment modified when a thin glass plate is introduced in the path of one of the interference waves?
d) ‘Diffraction limits the image forming capability of optical devices’. Discuss the authenticity of this statement for the particular case of a microscope.
e) Discuss the importance of hologram in (i) information storage, and (ii) pattern recognition.

2. a) A plane e.m. wave is incident normally on an interface. Obtain expressions for reflection and transmission coefficients.
b) Show that superposition of two linearly polarised light waves having different amplitudes and a finite phase difference can be used to produce elliptically plane polarised waves.
c) How is image formed on the retina of human eye processed by human brain? Discuss.

3. a) Discuss the principle of Michelson interferometer. How is it used to determine the refractive index of a thin plate?
b) Show that the radius of a dark Newton’s ring is directly proportional to the square root of the radius of curvature of the lens used.
c) The inclined faces of a glass biprism (μ = 1.5) make an angle of 1° with its base. The biprism is illuminated by a sodium lamp (λ = 589 nm) and the eye piece is at a distance of 1 m from the slit. A convex lens inserted between the biprism and the eye piece gives clear images of coherent sources in the focal plane of the eye piece. If the images are 0.4 cm apart in one case and 0.16 cm apart in the second case, calculate the width of interference fringes observed on the screen.

4. A vertical single and double slits are illuminated by a point source. Discuss the salient features of their Fraunhofer diffraction patterns. Also, obtain an expression for intensity distribution in case of double slit.

5. a) Discuss applications of lasers in medicine and communication.
b) Define numerical aperture and angle of acceptance. An optical fiber has a numerical aperture of 0.20 and cladding refractive index of 1.59. Calculate the refractive index of the core material and the acceptance angle of the fibre in water whose refractive index is 1.33.
c) With the help of a labelled diagram, discuss lasing action of a He-Ne laser.