please dont get afraid by the size of the question beleive me it is easy (give it a thought cmon)!!
ABOVE THE background neede to solve this one is given
the two questions are given below
i will tell the source later..
9hey satan i just proved it in previous post and ur telling that we cant prove it without given info?!!!!!
1i didnt say your solution was wrong :)
i said your description of the envelope was incomplete
9you have used concept that light is emitted at angle θ given in comprehension
then we can just like tell that given wavefront is perpendicular to light path without any derivation
i think ipho wants to derive that fact from abinitio
thats what i did in my solution
i dint use hint given in comprehension
9oh yes i was reffering to wavefronts intersection on plane
thats a line
1here is my solution
please make the figure youself
let at any point C at time t
between A and B the particle emits a light wave at an angle θ
then when the particle reaches B at t1
that wave has travelled c/n(t1-t)cosθ+vt in x direction
and c/n((t1-t)sinθ in y direction
eliminating the two eqautions we will get a straight lline with one point B and another at the coordinate
(c/n)t1cosθ,(c/n)t1csnθ
as this wave front will appear at all possible orientations of θ in the 3d space
rotating the line we get a CONE as the wave front envelope
further we see that vt1cosθ=vt1*(1/βn)=(c/n)t1
hence we get a right angled triangle
hence the envelope's projection onto a plane will be at an angle of 90-θ with the particle's trajectory
this question was from the International physics olympiad 2008
11isn't the wavefront a line making (π/2-θ) with the line along which the particle moves????????
9in the dia i showed only 2 close ones
imagine infinte close circles of dec radii one after other having com tangent as wavefont
am i clear to u:))
9its a superposition of diff spherical wave fronts giving a slope as in the above sol
im not concerning with pos of particle but with pos of wavefront from A at t
hence AC= ct/n
of course wavefront is a line inc;ined at φ
1but the wave front would not be spherical would it?
it is only emitting the rays at angle theta
imagine like a cirlce forming at all times
and AC is not ct/n it is vt
because it doesnot emit the rays having velocity ct/n at all angles only at angle theta
and rest part of your solution is not clear
ok if you had to draw the wave front what would u have drawn?
1you see read the question a bit more carefully
it is mentioned at an angle θ not at all angles!!
9yup i already found out
its superpositon of various circles giving parralel lines as their common tangent
cheronkov has derived something that even iit aspirants can derive!!!
1first u have to findout the shape of the wavefront ..
after that only you can go to the second part
9got it
φ = 90 - θ
do u want me to derive θ?
take the circles with diff radii and find common tangent
1i mean, ur box containning ur question is not fit in this page.
try to read question urself . u will know..............
