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Boss lesson · The Optics Bench
Exam-hall rules, last bench
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Exam-hall rules, last bench

This is the boss. No calculator: c=3.00×108 m/sc = 3.00 \times 10^8\ \mathrm{m/s}, the angles are pinned at 30° so sin⁡θ=12\sin\theta = \tfrac{1}{2} exactly, and every value on the bench is chosen to fit in your head. One laser travels the whole length of the course: the wave equation gives its frequency, the index gives its speed and wavelength inside a block, Snell's law bends it at the face, and Young's slits paint what is left on the wall.

Every answer feeds the next. Write each line down as you go — one early slip rolls all the way to the wall, and the finish will trace exactly where the cascade started. Two things to hold onto: the frequency never changes, whatever the light passes through; and a block with parallel faces hands the beam back to the air with its original wavelength and its original direction, merely shifted sideways.

Everything from the chapter rides in it. 5★ under par here is the chapter crown. Clock in.

λvf

v=fλv = f \lambda

  • vv= Wave speed (speed)
  • ff= Frequency (frequency)
  • λ\lambda= Wavelength (length)
Wave Speed (v = fλ) solver →
ncv

n=cvn = \frac{c}{v}

  • nn= Index of refraction
  • vv= Speed of light in the medium (speed)
Index of Refraction (n = c/v) solver →
θ1θ2n1n2

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2

  • n1n_1= Index of refraction (medium 1)
  • θ1\theta_1= Angle of incidence (angle)
  • n2n_2= Index of refraction (medium 2)
  • θ2\theta_2= Angle of refraction (angle)
Snell's Law of Refraction solver →
λdΔyL

Δy=λLd\Delta y = \frac{\lambda L}{d}

  • Δy\Delta y= Fringe spacing
  • λ\lambda= Wavelength
  • LL= Slit-to-screen distance
  • dd= Slit separation

each variable a length

Double-Slit Fringe Spacing solver →
no calculator in the boss room — the numbers are chosen to fit in your head