Q25 of 26 Page 1

(a) Define a wavefront.

(b) Using Huygens’ principle, draw the diagrams to show the nature of the wavefronts when an incident plane wavefront gets


(i)reflected from a concave mirror,


(ii)refracted from a convex lens.


(c) Draw a diagram showing the propagation of a plane wavefront from denser to a rarer medium and verify Snell’s law of refraction.


OR


(a)A concave mirror produces a real and magnified image of an object kept in front of it. Draw a ray diagram to show the image formation and use it to derive the mirror equation.


(b)A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is


(i)a convex lens of focal length 20 cm,


(ii)a concave lens of focal length 16 cm?


(a) A wave-front is defined as the locus of all points in a wave surface having a constant phase or same phase.


(b) Huygens principle states that every point in a wave-front is a source of secondary wavelet.


(i) The following diagram shows a wave-front reflected from a concave mirror.



(ii) The following diagram shows a wave-front refracted from a convex lens.




(c) The following diagram illustrates Snell’s law using Huygens principle.


In the figure, i is the angle of incidence, r is the angle of refraction.


Let the speed of light in two mediums be and . Let be the time taken by wavefront to travel distance BC.


Therefore,


Now, we draw an arc of radius of length from A. Next we draw a tangent from C to the arc. Creating .


From the figure,


In ,


In ,


Therefore,


Now, we know that the refractive index relates to the velocities as



Therefore, and


Hence,





Thus, Huygens principle can be used to prove Snell’s law of reflection.


OR


(a) The following diagram illustrates the image formation by a concave mirror.



As evident from the figure, and are similar.


Hence,



And and are similar.



From the figure,



Here,







Dividing both sides with uvf and rearranging we get



Which is the mirror equation.


(b) We know, the lens equation is



where, v is the image distance, u the object distance and f is the focal length.


Here it is given that the image distance, . We need to find the image distance in both the cases.


(i) given, focal length,




(ii) given, focal length,




More from this chapter

All 26 →
22

Define the electric resistivity of a conductor.

Plot a graph showing the variation of resistivity with temperature in the case of a (a) conductor, (b) semiconductor.


Briefly explain, how the difference in the behavior of the two can be explained in terms of number density of charge carriers and relaxation time.


 23 SECTI

Asha’s uncle was advised by his doctor to have an MRI (magnetic resonance imaging) scan of his brain. Her uncle felt that it was too expensive and wanted to postpone it. When Asha learnt about this, she took the help of her family and when she approached the doctor, he also offered a substantial discount. She thus convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The resulting information greatly helped his doctor to treat him properly.

Based on the above paragraph, answer the following questions:


(a)What according to you are the values displayed by Asha, her family and the doctor?


(b)What in your view could be the reason for MRI test to be so expensive?


(c)Assuming that MRI test was performed using a magnetic field of 0 �1 T, find the maximum and minimum values of the force that the magnetic field could exert on a proton (charge = ) that was moving with a speed of .


 24

(a) Derive the expression for the potential energy of an electric dipole of dipole moment placed in a uniform electric field .

Find out the orientation of the dipole when it is in (i) stable equilibrium, (ii) unstable equilibrium.


(b) Figure shows a configuration of the charge array of two dipoles. Obtain the expression for the dependence of potential on r for r >> a for a point P on the axis of this array of charges.


OR


(a)Define electric flux. Write its S.I. unit.


(b)Using Gauss’s law, obtain the electric flux due to a point charge ‘q’ enclosed in a cube of side ‘a’.


(c)Show that the electric field due to a uniformly charged infinite plane sheet at any point distant x from it, is independent of x.


 26

(a) Describe, with the help of a suitable diagram, how one can demonstrate that emf can be induced in a coil due to the change of magnetic flux. Hence state Faraday’s law of electromagnetic induction.

(b) Two loops, one rectangular of dimensions 10 cm x 2 �5 cm and second of square shape of side 5 cm are moved out of a uniform magnetic field perpendicular to the planes of the loops with equal velocity as is shown in the figure.


(i)In which case will the emf induced be more?


(ii)In which case will the current flowing through the two loops be less?


Justify your answer.


OR


(a)State the principle of an a.c. generator.


(b)Explain briefly, with the help of labelled diagram, its working and obtain the expression for the emf generated in the coil.


(c)Draw a schematic diagram showing the nature of the alternating emf generated by the rotating coil in the magnetic field during one cycle.