
#1
Sep2011, 07:36 AM

P: 391

I finally found something about thin prisms on the web
Is the thin prism always in the position of minimum deviation? 



#2
Sep2011, 07:41 AM

P: 882

If you want to get understanding (rather than get ready answer to simplified yes/no question)  compute it yourself.
Compute what is deviation angle as a function of angle of incidence and apical angle, then make several plots (for several apical angles, e.g. 10°, 20°, 30°, 45°): deviation angle as a function of angle of incidence. And compare the plots. That's pretty easy calculation. You know Snell's law. You can do it yourself! Yes, you can! 



#3
Sep2011, 07:48 AM

P: 391

You are right,I already tried something like that,but I failed .I always get different angles of deviation for different angles of incidence,and this should not happen,because we study that the angle of deviation in a thin prism isn't affected by the angle of incidence.




#4
Sep2011, 07:53 AM

P: 882

Ray tracing a thin prism
Please, post the plots you made and formulae you got  I'll try to point out what you did wrong.




#5
Sep2411, 07:02 AM

P: 391

That's my workvery sorry for the bad resolution
I drew two diagrams At A=45 degrees  At A=10 degrees The first graph looks logical but there's a math error the second one looks very strange I don't know any laws about thin prism ,so I drew the angles manually,and at every angle of incidence,the angle of deviation has a different value.It's not supposed to be so according to the relation alpha=A(n1) so the angle of deviation is only dependent on the angle of the prism and the refractive index Hope you could find the problem with the second graph Thanks 



#6
Sep2611, 04:24 AM

P: 391

I've put my work as you told me,so could you tell me what's wrong with it?




#7
Sep2611, 05:20 AM

P: 882

First graph looks reasonably, the second is totally wrong  check calculations (the calculator may help)
You should find first the formula describing the deflection angle as a function of incidence angle and apical angle, then make several graphs of this formula for various fixed values of apical angle. You may want to use any computer program for drawing graphs of functions (you'd probably been taught one of such programs at school  but even excel can do this), rather than computing all that trigonometry by hand... 



#8
Sep2611, 05:52 AM

P: 391





#9
Sep2611, 05:56 AM

P: 882

Derive a general formula, describing the deflection angle as the function of two parameters: apical angle and incidence angle.
Derivation is pretty easy. You must just draw a picture, give names (symbols, rather than actual values in degrees) to all angles, then combine and reduce several simple trigonometrical formulae. 



#10
Sep2611, 05:56 AM

P: 391

do u mean that
Apical angle=second Angle of incidenceAngle of refraction? This is just for thin prism I guess. How about math errors in both graphs 



#11
Sep2611, 06:08 AM

P: 882





#12
Sep2611, 06:34 AM

P: 391

Could you explain more:( I still can't imagine what I have to do 



#13
Sep2611, 06:47 AM

P: 391

I checked the numbers in the second graph,there's nothing wrong with them
Could you give me some laws about thin prism to use them instead of drawing the prism manually? 



#14
Sep2611, 06:55 AM

P: 882

You may easily derve Misr's law: the law describing deflection angle of the prism... first:Is the equation I wrote correct?  you haven't wrote the equation, except of sime sidenotesyou used in calculations, but as you haven't presented it as a part of ordered reasoning, I can't judge them. I still can't imagine what I have to do Make a drawing how the ray passes through a prism. Something like in your first post. Mark all angles and give them symbols. Write down Snell's relations between incidence/refraction angles on both surfaces, using n as refraction index. Express all angles as sums/differences of: apical angle, incident angle on first surface, deflection angle.Transform those equations to have it in form: deflection_angle = some_function_of(incident_angle, apical_angle, n) Make graphs of that function for several fixed values of apical_angle and single example value of n Compare those graphs visually and find some regularity of the graph shapes  it will be obvious as you look at the graphs. 



#15
Sep2611, 11:10 AM

P: 391

you mean by "deflection angle" the angle of deviation?




#16
Sep2611, 11:49 AM

P: 882





#17
Sep2611, 02:54 PM

P: 391

I've been working on this for hours
I derived two equations but there's something wrong with them deviation angle=angle of emergence angle of incidence+Apical angle This works on some values of angle of incidence but while making some calculations I found that's not trueit gives me a negative value for the angle And it is the same for Apical angle=Angle of refractionsecond angle of incidence Could you help me with signs because I'm getting very bored 



#18
Sep2711, 04:57 AM

P: 882

I see you got lost in it. A little help from my side  I spent 10mins to make a readable drawing: In this convention your equation is:[tex]\delta=\theta\beta\alpha[/tex] 


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