Q. 1. Distinguish between forced and free vibrations. Give theory of free damped vibrations. Explain the behaviour under large and small damping.
Q. 2. (a) What are normal co-ordinates and normal modes?
(b) Image no.1
In the above figure the 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, find :
(i) Normal modes for vibrations;
(ii) Normal co-ordinates for longitudinal vibrations.
Q. 3. (a) State Fermat’s principle and derive laws of refraction based on Fermat’s principle.
(b) Discuss Huygen’s principle and derive laws of reflection based on this principle.
Q. 4. (a) Explain with derivation as to how one determines me refractive index of a transparent liquid with Newton’s rings set-up. Comment on the central fringe in case of Newton rings set-up in reflected mode. 5
(b) In Newton rings experiment the diameter of 10th ring changes from 1.4 cm to 1.3 cm when a liquid is introduced be¬tween the lens and plate. Calculate the refractive index of the liquid.
Q. 5. (a) Discuss the Fraunhofer diffraction due to double slit. Explain, what do you mean by missing orders. 5
(b) What should be the minimum number of lines in a diffraction grating which will just resolve in second order the lines laving wavelengths 5890 A and 5896 A ?
Q. 6. (a) Explain the action of zone plate. Compare it with a lens. Describe, how a zone plate can be constructed. 5
(b) Distinguish between normal and anomalous dispersion.
Q. 7. (a) Explain the term cardinal points with reference to co-axial lens system. 4
(b) A co-axial system has two lenses of focal lengths 3F and F separated by a distance 2F. Find out the position of cardinal points.
Q. 8. Write short notes on any two of the following
(i) Gravity waves;
(ii) Superposition of waves;
(iii) Wood’s experiment;
(iv) Ramsden and Huygen’s eyepieces.