Light And Modern Physics Formula Sheet 1u1xi

Relationships:   𝑐 𝑣 = 𝑓𝜆 =   𝑛 bright

!

dark 𝑑 sin 𝜃! = 𝑚 + ! 𝜆; 𝑚 = 0, ±1, ±2, …  

= 𝑚𝜆; 𝑚 = 0, ±1, ±2, …  

𝑑 sin 𝜃!

dark 𝑎 sin 𝜃! = 𝑚𝜆; 𝑚 = 0, ±1, ±2, …  

𝜃min =

𝑦! = 𝐿 tan 𝜃!  

𝜆 , 𝑎

𝑛! sin 𝜃! = 𝑛! sin 𝜃!   ℎ! 𝑞 𝑀 = = −   ℎ 𝑝

𝑛!  (for  𝑛! > 𝑛! )   𝑛!

𝑓 𝑓-­‐number =   𝐷

1 1 2 1 + = =   𝑝 𝑞 𝑅 𝑓

1 = 𝑛−1 𝑓

𝜆! − 𝜆! =

ℎ 1 − cos 𝜃   𝑚! 𝑐

𝐾max = ℎ𝑓 − 𝜙   ℎ 𝜆 =   𝑝

ℏ ∆𝑝∆𝑥 ≥   2 !

𝑥 =

ℏ! 𝑑 ! 𝜓 + 𝑈𝜓 = 𝐸𝜓   2𝑚 𝑑𝑥 ! ℎ! 𝐸! = 𝑛! ; 𝑛 = 1, 2, 3, …   8𝑚𝐿!

𝜓 ∗ 𝑥𝜓 d𝑥  

−

!!

𝑛𝜋𝑥 ; 𝑛 = 1, 2, 3, …   𝐿

1 1 1 = 𝑅H ! − ! ; 𝑛 = 3, 4, 5, …   𝜆 2 𝑛

1 1 −   𝑅! 𝑅!

𝜆max 𝑇 = 2.898×10!! m∙K  

𝐸 = ℎ𝑓  

𝜓 𝑥 = 𝐴 sin

𝜆 𝜃min = 1.22   𝐷

𝑛!   𝑛!

tan 𝜃p = sin 𝜃! =

∆𝑥 + ∆𝜙!   𝜆

∆𝜙 = 2𝜋

𝐸! = −

𝑘! 𝑒 ! 1 13.606  eV =− ; 𝑛 = 1, 2, 3, …   ! 2𝑎! 𝑛 𝑛!

𝐸! = 𝑍𝑀 𝐻 + 𝑁𝑚! − 𝑀 !!𝑋 ×931.494  MeV/u   𝑁 = 𝑁! 𝑒 !!" ; 𝑅 = 𝑅! 𝑒 !!"  

𝑇!

!

=

0.693   𝜆

Constants:   𝑚e = 5.48579×10!!  u = 9.10938×10!!"  Kg  

1eV = 1.60×10!!"  J  

𝑚p = 1.007276  u = 1.67262×10!!"  Kg  

𝑒 = 1.60×10!!"  C  

𝑚n = 1.008665  u = 1.67493×10!!"  Kg  

ℎ = 6.63×10!!"  J∙s  

1  u = 1.660539×10!!"  Kg = 931.494  MeV/𝑐 !  

ℏ=

𝜎 = 5.67×10!!  W/m! ∙K !  

ℎ𝑐 = 1240  eV∙nm  

ℏ! 𝑎! = = 0.0529  nm   𝑚! 𝑘! 𝑒 !

𝑘! = 8.9876×10!  N∙m! /C !  

𝑅H = 1.0973732×10!  m!!  

𝑐 = 2.99792×10!  N∙m! /C !  

 

 

10  

ℎ = 1.055×10!!"  J∙s   2𝜋