Q. 1. Distinguish between free and forced vibrations. Give theory of forced damped vibrations. Discuss the condition of resonance.
Q.2 Image no. 2
In the above figure two masses ma and mb are connected by three massless springs of spring-constants k1, k2 and k3 If ma = mb = m and k1 = k2 = k3 = k :
(i) Find frequency of normal modes for longitudinal vibration.
(ii) Find normal co-ordinates for longitudinal vibration.
(iii) Show that the total energy of the system is equal to the sum of energies associated with the two modes.
Q. 3. (a) What is optical path ? State Fermat’s principle and derive laws of reflection based on Fermat’s principle. 4
(b) State Huygen’s principle and derive laws of refraction from Huygen’s principle.
Q. 4. (a) What are Newton’s rings and how are they formed? How would you use Newton’s rings to measure wavelength of light? 5
(b) In Newton’s rings experiment the diameter of 10th ring changes from 1.5 cm to 1.4 cm when a liquid is introduced between the lens and plate. Calculate the refractive index of the liquid.
Q. 5. (a) What do you mean by Fraunhoffer diffraction ? Describe the Fraunhoffer pattern obtained with a single slit illuminated by a beam of monochromatic light. Deduce condition of maxima and minima.
(b) Calculate the minimum number of lines in a grating which will just resolve the two wavelengths 5890 A 5896 A in its first order.
Q. 6. (a) Describe the construction of a zone plate and explain its working. Explain how it behaves as a lens of multiple foci. 5
(b) Distinguish between normal and anomalous dispersion.3
Q. 7. (a) Derive an expression for the equivalent focal length of two lenses separated by a distance. 5
(b) Two thin convex lenses having focal lengths 5 cm and 2 cm are co-axial and are separted by a distance of 3 cm. Find the equivalent focal length and position of cardinal points.
Q. 8. Write short notes on any two of the following :
(i) Lissajous figures;
(ii) Melde’s experiment;
(iii) Temporal and spatial coherence;
(iv) Chromatic and spherical aberrations.