SLIDE 35 ■♥tr♦❞✉❝t✐♦♥ ❛♥❞ ♠❛✐♥ r❡s✉❧t ❚❤❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♦♥ ❈❤❛♥❣✐♥❣ tr✐❛♥❣✉❧❛t✐♦♥s
❚❤❡ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♦♥
❲❡ ❝♦♥s✐❞❡r ❛ ♣♦❧②❤❡❞r♦♥ P ✇✐t❤ ❛ tr✐❛♥❣✉❧❛t✐♦♥ ❚✱ ❛♥❞ ❞❡❢♦r♠❛t✐♦♥s ✇❤✐❝❤ ✈❛r② t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ✐♥t❡r✐♦r ❛♥❣❧❡s✱ ✜①✐♥❣ t❤❡ ❜♦✉♥❞❛r② ♠❡tr✐❝✳ ❈♦♥❡ s✐♥❣✉❧❛r✐t✐❡s ❛♣♣❡❛r ♦♥ t❤❡ ✐♥t❡r✐♦r ❡❞❣❡s ✿ t♦t❛❧ ❛♥❣❧❡ ✐s ♥♦t ✷π✳ ❉❡❢ ✿ ❙ =
❧❡(✷π − θ❡) −
❧❡α❡ , s✉♠ ♦✈❡r ✐♥t❡r✐♦r r❡s♣✳ ❜♦✉♥❞❛r② ❡❞❣❡s✳ ❍✐❧❜❡rt✲❊✐♥st❡✐♥ ❢✉♥❝t✐♦♥✱ ❛❦❛ ❘❡❣❣❡ ❢✉♥❝t✐♦♥✱ ❡t❝✳ ❚❤❡ ❙❝❤❧ä✢✐ ❢♦r♠✉❧❛ ✿ ∀ ❞❡❢♦r♠❛t✐♦♥ ♦❢ ❛ ♣♦❧②❤❡❞r♦♥✱
❧❡❞θ❡ = ✵ . ❙♦ ❞❙ =
✐(✷π − θ✐)❞❧✐✱ ❛♥❞ t❤❡ ❍❡ss✐❛♥ ♦❢ ❙ ✐s −▼❚ = −(∂θ✐/∂❧❥)✳
❘❡♠❛r❦ ✭❇❧❛s❝❤❦❡✱ ❍❡r❣❧♦t③✮ ✿ ✐❢ ❚ ❤❛s ♥♦ ✐♥t❡r✐♦r ✈❡rt❡①✱ P ✐s ✐♥❢ r✐❣✐❞ ✐✛ ▼❚ ✐s ♥♦♥✲❞❡❣❡♥❡r❛t❡✳
❏❡❛♥✲▼❛r❝ ❙❝❤❧❡♥❦❡r ❖♥ t❤❡ r✐❣✐❞✐t② ♦❢ ✇❡❛❦❧② ❝♦♥✈❡① ♣♦❧②❤❡❞r❛