another small conceptual

hey satan i just proved it in previous post and ur telling that we cant prove it without given info?!!!!!

i didnt say your solution was wrong :)

i said your description of the envelope was incomplete

you 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

here 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

isn't the wavefront a line making (π/2-θ) with the line along which the particle moves????????

but 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?

no celestine.. that is not wave front

wats thje source

yup 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!!!

first u have to findout the shape of the wavefront ..
after that only you can go to the second part

no it is!

the second image is just a continuation to the first!!