 5
 1
 Homework Statement

Show that, for any angle of incidence on a prism, following equation is true:
and and that the righthand side reduces to μ' at minimum deviation.
 Homework Equations

sin[(A+d)/2]/ sin(A/2) = μcos[(r1r2)/2]/ cos[(ie)/2]
A = Angle of Prism
d = Total deviation by Prism
i= Angle Of First incident ray
e= Angle Of Final emergent Ray Corresponding to i
where
r1= Angle Of First refracted ray
r2= Angle Of Ray incident on second surface whose refracted ray makes angle e
μ= refractive index of prism relative to air
I've tried to attempt the first part of the problem(spent over an hour on this) as second part could be easily optained with some calculus ,I asked my friend but alas nobody could conjure the solution to this dangerous trigonometric spell.
It was just pages and pages of concoction of trigonometric manipulation with no end in sight so I think it is of no use to print my attempt here
My Thought Process: 1.) Begin with lhs, expand using sum trigonometric identity and substitute μ to arrive at something reducible to rhs
=>Failed
2.) Try to reverse engineer the rhs into lhs , do the same circus trick of substituting μ(in in trig expression) but nothing worked
=>Failed
3.) gOOGled but found nothing except out of print solution manuals available only in libraries :(
Regards,
BrazenHammer
It was just pages and pages of concoction of trigonometric manipulation with no end in sight so I think it is of no use to print my attempt here
My Thought Process: 1.) Begin with lhs, expand using sum trigonometric identity and substitute μ to arrive at something reducible to rhs
=>Failed
2.) Try to reverse engineer the rhs into lhs , do the same circus trick of substituting μ(in in trig expression) but nothing worked
=>Failed
3.) gOOGled but found nothing except out of print solution manuals available only in libraries :(
Regards,
BrazenHammer