Q. 25

(a) Define a wave

Answer :

(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,




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