Final Exam Equations

Geometric Optics

100

Law of Reflection

θ_r= θ_a

200

Law of Refraction

n_asinθ_a= n_bsinθ_b

300

Index of Refraction

n= c/v

400

Wavelength

λ= λ₀ /n

500

Critical Angle

sinθ_c= n_b / n_a

Geometric Optics pt. 2

100

Brewster's Angle

tanθ_p = n_b/n_a

200

Thin Lens/Mirror Equation

1/s + 1/s' = 1/f

300

f

f=R/2

400

 Lateral Magnificattion

m= y'/y = s'/s

500

Lensmaker's Equation

1/f = (n-1)(1/R₁ - 1/R₂)

Geometric Optics pt. 3

100

Small Angle (paraxial) Approximation.

sinθ = θ = tanθ = y/R

200

Malus's Law

 I = I_maxcos²Φ

300

Angular Magnification of a Magnifying Glass

M = θ'/θ = 25cm/f

Wave Optics

100

Phase Difference Between Two Rays.

Φ= 2π/λ Δr + (Φ₂ - Φ₁)

constructive: Φ= 0, 2π

destructive: Φ = π, 3π

200

Constructive Interference for a Double Slit

dsinθ = mλ 

300

Constructive Interference for Diffraction Gratings

dsinθ = mλ

400

Intensity of Two-Source Interference

I =I₀cos₂ (Φ/2)

500

Path Length Difference for Thin Film Reflection

 Δr= 2t

Wave Optics pt. 2

100

Angular Radius of the First Dark Ring (Rayleigh criterion)

sinθ₁ = 1.22(λ/D)