← Physics II: E&M and Waves

Unit 14: Wave Optics

What geometric optics leaves out: light interfering with itself through two slits and a thin film, bending around every edge, one photon at a time.

11 topics · 38 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Huygens's Principle

  1. How it worksHow does treating every point on a wavefront as a source of its own tiny wavelets predict how the whole wave moves next?
  2. How it worksWalk me through using Huygens's principle to explain why a wavefront bends slightly as it passes an edge.
  3. Ties togetherHow does Huygens's principle explain both the law of reflection and Snell's law as two special cases of one idea?
Your turn1 of 2
According to Huygens's principle, how does a wave's overall shape propagate forward from one instant to the next?

Coherence and Interference

  1. How it worksHow does a fixed phase relationship between two sources let their waves reliably add up or cancel at fixed points?
  2. Common mistakeWhy doesn't shining two separate flashlights on the same wall ever create visible interference fringes?
  3. Ties togetherHow does coherence become the missing ingredient that turns ordinary wave superposition into a stable pattern?
Your turn1 of 2
Why doesn't shining two separate ordinary flashlights on the same wall ever create a visible, stable interference pattern?

Young's Double-Slit Experiment

  1. How it worksHow do waves from two slits arrive in step at some points on a screen and out of step at others?
  2. Worked exampleFind the position of the third bright fringe on a screen 2 meters away, using slits 0.2 mm apart and 600 nanometer light.
  3. Common mistakeWhy doesn't Young's double-slit result make sense unless light is treated as a wave, not particles moving straight?
  4. Going furtherWhat happens to the fringe spacing in a double-slit pattern if the slit separation is made smaller?
Your turn1 of 2
Find the position of the 4 order bright fringe on a screen 4 meters away, using slits 5 times 0.1 mm apart and 484 nanometer light.

Double-Slit Fringe Spacing

  1. How it worksHow does the path difference between two slits reaching a screen point set exactly where bright and dark fringes fall?
  2. Worked exampleFind the wavelength of light producing bright fringes spaced 3 mm apart on a screen 1.5 meters from slits 0.15 mm apart.
  3. Going furtherWhat happens to the spacing between bright fringes if red light is swapped for shorter-wavelength blue light?
Your turn1 of 2
Find the wavelength of light producing bright fringes spaced 4 mm apart on a screen 2 meters from slits 3 times 0.1 mm apart.

Multiple-Slit Interference

  1. How it worksHow does light from many slits add up constructively at the same fringe locations two slits would give, but far more sharply?
  2. Worked exampleFind the angle of the first-order bright fringe from a grating of 5000 lines per centimeter using 500 nanometer light.
  3. Going furtherWhat happens to the sharpness of the bright fringes as the number of illuminated slits keeps increasing?
Your turn1 of 2
Find the angle of the first-order bright fringe from a grating of 5875 lines per centimeter using 595 nanometer light.

Thin-Film Interference

  1. How it worksHow do reflections off a thin film's top and bottom surfaces interfere constructively for some wavelengths and destructively for others?
  2. Worked exampleFind the minimum soap film thickness, index 1.33, that destructively interferes with 550 nanometer light viewed head-on.
  3. Common mistakeWhy does a reflection off a thin film sometimes flip phase by half a wavelength and sometimes not, depending on the interface?
  4. Going furtherWhat happens to a soap film's interference colors as the film drains and grows thinner right before it pops?
  5. Worked exampleFind the minimum thickness of a non-reflective coating of index 1.38 on glass for light of wavelength 550 nanometers.
Your turn1 of 2
Find the minimum soap film thickness, index 137 times 0.01, that destructively interferes with 595 nanometer light viewed head-on.

The Michelson Interferometer

  1. How it worksHow does a Michelson interferometer split a beam, send it down two paths, and recombine it to reveal a tiny path difference?
  2. Worked exampleFind how many fringes shift past a point when one mirror moves 0.001 mm, using light of wavelength 500 nanometers.
  3. Ties togetherHow does the Michelson interferometer apply thin-film-style interference to two full light paths instead of two surfaces?
Your turn1 of 2
Find how many fringes shift past a point when one mirror moves 1423 nanometers, using light of wavelength 595 nanometers.

Single-Slit Diffraction

  1. How it worksHow do different parts of the same slit's own wavefront interfere with each other to create a diffraction pattern?
  2. Worked exampleFind the angle to the first dark fringe in a single-slit pattern using a 0.02 mm slit and 600 nanometer light.
  3. Common mistakeWhy doesn't a single narrow slit need a second slit nearby to still produce its own diffraction pattern?
  4. Going furtherWhat happens to a single-slit diffraction pattern as the slit itself is made narrower and narrower?
Your turn1 of 2
Find the angle to the first dark fringe in a single-slit pattern using a 4 times 0.01 mm slit and 595 nanometer light.

Intensity in Single-Slit Diffraction

  1. How it worksHow does adding up wavelets across a slit's width with different phases produce an intensity pattern that fades from the center?
  2. Worked exampleFind the ratio of the central maximum's width to the first secondary maximum's width in single-slit diffraction.
  3. Going furtherWhat happens to the width of the central maximum as the slit itself is made wider?
Your turn1 of 2
In a single-slit diffraction pattern, how does the angular width of the central bright maximum compare to the angular width of one of the secondary, side maxima?

Diffraction Gratings

  1. How it worksHow does a diffraction grating's thousands of closely spaced lines pick out very sharp bright fringes at specific angles?
  2. Worked exampleFind the wavelength sent into a grating's first-order bright fringe at 15 degrees, using 3000 lines per centimeter.
  3. How it worksWalk me through why X-ray diffraction off a crystal's regularly spaced atomic planes uses this exact grating equation.
  4. Ties togetherHow does a diffraction grating extend the two-slit interference idea to thousands of slits acting together at once?
Your turn1 of 2
Find the wavelength sent into a grating's first-order bright fringe at 29 degrees, using 4245 lines per centimeter.

Resolution and the Rayleigh Criterion

  1. How it worksHow does diffraction at a telescope's circular aperture set a fundamental limit on how sharply it can resolve two objects?
  2. Worked exampleFind the minimum angular separation resolvable by a 10 cm telescope aperture using light of wavelength 550 nanometers.
  3. Going furtherWhat happens to a telescope's resolving power as its aperture diameter is made larger?
Your turn1 of 2
Find the minimum angular separation resolvable by a 35 cm telescope aperture using light of wavelength 595 nanometers.