Very important questions of wave optics

Very important questions of wave optics –

Long answer type questions (3 and 5 marks)-

1. Define wave-front . What type of wave front will emerge from a point source and distance light source? Draw a wave front coming out from a (I)prism(II)concave and convex mirror(III)concave lens and(III)convex lens .
2. State Huygens principle, using this principle draw the diagram to show how a plane wave front  incident(I) At the interface of two media gets refracted when it propagates from a rarer to denser medium, and hence verified Snell’s law and (II) At a plane surface and gets reflected and hence derive law of reflection.
3. What are coherent sources of light ? Why two independent sources can’t be coherent ?why coherent sources are necessary to observing a sustained interference pattern ? How are the coherent sources are obtained in the Youngs double slit experiment?
4. What is interference of light? Write dawn the conditions to obtain the sustained interference fringe pattern. Show that the superposition of wave originating from two sources   having displacement                Y₁ =a cosωt  , Y₂ =a cos(ωt+ɸ) at a point produces a resultant intensity ,I=4a² cos²(ɸ/2) hence write the conditions for the appearance of dark and bright fringes.(* this question may be asked as deduce the conditions for constructive and destructive interference and hence write the expression for the distance between two consecutive bright or dark interference)
5. Using Youngs double slit experiment obtain the conditions for gating bright and dark fringes  also derive the expression for the fringe width.  Also write the effect on fringe width when(I)Distance between slits increases/decreases (II) Distance between slits and the screen increases/decreases(III) Monochromatic light replaced  by white light,(IV) One of slit is closed and (V) entire experimental apparatus is immersed in a liquid
6. In a single slit diffraction experiment , deduce the conditions for the central maximum and secondary maxima/minima observed in diffraction pattern . Also explain why the secondary maxima go on becoming weaker in intensity as the order increases.(I) Haw does the width of the slit affected the size of the central bright fringe?(II)When a tiny circular obstacle is placed in the path of the light from a distant source , why is a bright spot seen at the centre of the shadow of the obstacle?(III) Show that the angular width of the central bright is two times the width of the first diffraction fringe (IV) If a mono chromatic source of light is replaced by white light , what change would you observe in the diffraction pattern?
7. In a modified setup of  YDS experiment , it is given that     SS₂  –  SS₁ =  λ/4 . (I) Obtain the condition for constructive and destructive interference at a point P on the screen in terms of the path difference მ = S₂P -S₁P . (II) Does the observed central bright fringe lie above or below O ? Give reason in support of your answer .