Prove refractive index of prism (help please )

[JonnyRockets]

Refractive Index Problem invloving prism (Please Help)

Homework Statement

What is given is a prism, angle of deviation and apex angle, I also have to find refractive index of the prism.

To solve the problem I must prove that:
Nprism = sin((A+d)/2)/ sin(A/2)


The diagram given of the Prism:
http://img80.imageshack.us/img80/5148/trianglepv4.png

Homework Equations

n sin(i) = nprism sin (r)


3. My attempt at a solution

nprism = sin(i1)/sin(r1)


therefore i1 = (A+d)/2 and r1 = (A/2)


just need to figure i1 = (A+d)/2 and r1 = (A/2) by proving


Please Note: My solution so far may be completely wrong, any help given would be very much appreciated :)

 

[JonnyRockets]

Does anyone have any Ideas on how to solve this, maybe a more advanced physics member on this forum may be able to shed some light on this question?

 

[malawi_glenn]

where is d in your figure?

 

[JonnyRockets]

Sorry here is the new triangle with d, please if anyone knows how to solve this question it would be very much appreciated :)

http://img242.imageshack.us/img242/6923/trianglepv4oy9.png

 

[jini]

in minimum deviation position:
i1=r2
r1=i2 say =r
thus, A=2r implies r=A/2
and from equation
d+A=i1+r2 (similarity of triangles and geometry)
i1+r2=A+d
thus, i=(A+d)/2

refractive index n=[sin(A/2 + d/2)] / [sin(A/2)]
since, n=[sin i1] / [sin r]hope it helped