1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Optics problem

  1. Mar 12, 2014 #1
    1. The problem statement, all variables and given/known data
    Using the results of Problems 4.70, that is EQs. (4.98) and (4.99), show that

    Rparallel + Tparalllel = 1

    2. Relevant equations

    Rparallel = ( tan^2 ( thetai - thetat) ) / (tan^2 (thetai + thetat) )

    Tparallel = (sin (2*thetai) * sin (2*thetat))/ sin^2 (thetai + thetat)

    3. The attempt at a solution

    After getting this far (shown below) I took it to the math help center at my university and they couldn't solve it any further than what I had done:

    First put both in the same denominator

    sin^2 (thetai - thetat)) / cos^2(thetai - thetat) * cos^2(thetai + thetat/sin^2(thetai + thetat which gives a common denominator of cos^2(thetai-thetat)* sin^2(thetai + thetat)

    For brevity I will call thetai = i and thetat = t

    Now we have sin^2(i-t)*cos^2(i+t) + sin (2*i)*sin(2*t)/ cos^2(i-t)*sin^2(i+t)

    I tried (1 - cos^2(i-t)*(1-sin^2(i+t) + sin(2*i)*sin(2*t)/ cos^2(i-t)*sin^2(i+t)

    which puts the minus on cos and plus angle on sin which matches the denominator but that is as far as I got which was further than the help desk at my university.

    Can someone give me a hint as to which identities I should use to work this out?

    You have my undying gratitude and about a million photons of positive energy sent to you for your help!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Mar 14, 2014 #2
    Here's two identities that might help:

    ##\sin^2(x-y) = \sin^2(x+y) - \sin(2x)\sin(2y)##
    ##\cos^2(x-y) = \cos^2(x+y) + \sin(2x)\sin(2y)##
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted