Q. A transparent sphere of radius R and refractive index n is at rest on a horizontal surface. A ray of light is incident parallel to the vertical diameter and at a distance d from it.
a) Obtain an expression for d in terms of n and R such that the ray intersects the diameter at the point of emergence.
b) What is the allowed range of values of n for the above possibility to occur??
This ques. came in this year's Indian National Physics Oly. Plzzzz try solving this ques. and tell me the answer.
I got the answer as d = [nR(4-n2)1/2]/2
and the allowed range of n as (1,2).
Well Ankul I got the samething
d=[nR(4-n2)1/2]/2 & about n obvously (1,2)
Well the result is consistent with the limitations of as if u observe always d<R equality occuring iff n=21/2
More over total internal reflection is absent. May be u did observe all this .Its such simple one any ways why did someone like u ask this.
Anyways what troubles u MAN
Well actually my frnd got some other answer and thats why i thought why not get it clarified.....
Otherwise i also tried it myself 3-4 times and couldn't find any mistake...
Thnxxxxx man for the reply
Otherwise i also tried it myself 3-4 times and couldn't find any mistake...
Thnxxxxx man for the reply
Well tell me what your friend has got may be we both are doing the same mistake
Well i have clarified with him... he did some mistake... not us.... :)
Well one more thing.... shall we include n=1 and 2 in the range of n or not.....
Because for n = 2... d = 0 and for n = 1..... d is not = 0 which should be the case otherwise... what do you say??
Well one more thing.... shall we include n=1 and 2 in the range of n or not.....
Because for n = 2... d = 0 and for n = 1..... d is not = 0 which should be the case otherwise... what do you say??
Sorry for the late reply man just got busy
Anyways if n=2 is included then i think we need to inclde every number greater than 1 as a solution keepin d=0 which is obviously dumb so I dont recomend 2 thats the reason for the open interval in my answer .I too did observe that n=1 is givin something stupid acually while solvin I was forced to make an assumption tht n is different from 1 and after getting the solution obvously u wil check for extreme values as they do matter a lot hence n=1 is rejected. So i would say N belogs to(1,2)
Ayways da i am quite impressed by the way u and chandni
Reason out ur answers(I was referrin to older disscussions)
thnx for dat dude..... but still the confusion prevails in this ques.
This ques. doesn't seems to be that easy..... dont know the exact reason but some ppl r saying that the answer should be (21/2 to 2). Lemme confirm it how they were getting root 2 in the picture.... some were saying that the formula would not be valid for n above 1 and below 21/2.
I wud request u to think over the situation again. Actually while simplifying for d in terms of n and R we actually square both the sides 2 times.... i think u wud have also done that.... so that way some extra roots would also be coming.... well n = 1 is one such root.... i think other roots are okey.... still i wud fix myself wid (1,2)... but just check it once again...
This ques. doesn't seems to be that easy..... dont know the exact reason but some ppl r saying that the answer should be (21/2 to 2). Lemme confirm it how they were getting root 2 in the picture.... some were saying that the formula would not be valid for n above 1 and below 21/2.
I wud request u to think over the situation again. Actually while simplifying for d in terms of n and R we actually square both the sides 2 times.... i think u wud have also done that.... so that way some extra roots would also be coming.... well n = 1 is one such root.... i think other roots are okey.... still i wud fix myself wid (1,2)... but just check it once again...
Ya dude thts right we are invitinng unnessasary solutions into our equations by squarin
I got somethin like this
(R2-d2)1/2=R(n2-2)/2
Which we further square 2 arrive at ur final answer but the thing here is R.H.S has 2 be +ve as L.H.S is +ve
Hence before squarin itself we need 2 observe that n should not be less than 21/2.
well i didnt observe all this as i was thinkin that this problem was dumb But it seems that we both have commited the same mistake.
Well i do have anothher way of sayin why its > 21/2
But that is really TEEEEEEEEEEEEDIOUS( beleive me Its a real tough eqn to solve) well lets just use continuity theorom and be satisfied with [21/2,2)
Anyways man thnx i am known for doing calculation mistakes but i never do logical errors,May be after a long time i have done it again in PHYSICS.I AM A PHYSICS FREAK
I may seem to be a very stupid girl because I could not understand the question itself . Can somebody explain me what the question is saying?
The question is that if a ray of light parallel to the vertical diameter of a sphere of refractive index 'n', but at a distance 'd' (d<=R) falls on the sphere and after refraction from the sphere reaches the other end of the vertical diameter. Find the condition on n,R, d for the above possibility.