OPOpenPithMake curiosity visiblePhysics lab / Optics

About this lab

Seven experiments, two models of light.

The first five experiments use rays: light travels in straight lines, reflects and refracts at a boundary, and a lens brings a beam back together. The last two use waves: light through two slits overlaps into bright and dark fringes, and a polarizer passes only one direction of vibration. Rays answer where light goes; waves answer where it is bright.

Every reading, dot and curve comes from the same physical model, not a pre-drawn animation. Change one parameter and all the data is recalculated together.

Seven conclusions

Each experiment overturns a common idea.

The angle of incidence is the angle to the mirror?

The angle of incidence is measured from the normal. At 30° incidence the reflection angle is also 30°, while the ray makes 60° with the mirror. Fold the right half of the board back and the reflected ray disappears from it.

Step back and your image shrinks?

Image size does not depend on distance. Moving the candle from 5 cm to 30 cm, the image stays 8.0 cm tall; what shrinks is the viewing angle, from 12.3° to 7.4°.

Refraction angle proportional to incidence?

From air into glass at 10°, 30°, 50° and 70°, sin i / sin r is always 1.50 while i / r climbs from 1.50 to 1.80. It is the sines that are proportional.

The refracted ray switches off suddenly?

From glass to air, as the incidence angle rises from 0° to 5° short of critical, the refracted energy falls from 96.0% to 88.7%; then it fades fast and reaches 0 at the critical angle of 41.8°, while the reflection rises to 100%.

Cover half the lens, lose half the image?

With u = 30 cm and f = 10 cm the image is real, inverted and reduced, 15.0 cm from the lens. Covering the top half changes neither distance nor height: the image is whole, at 50% brightness.

Two slits make two bright lines?

With 650 nm red light, d = 0.20 mm and L = 0.80 m the screen shows a row of fringes 2.60 mm apart. Measuring across 6 gaps gives λ = 650 nm.

A third polarizer can only darken?

Crossed polarizers pass nothing; put a 45° sheet between them and 25% of I₁, or 12.5% of the natural light, gets through.

Model and sources

Model and sources

  • Reflection: incident ray, normal and reflected ray are coplanar, r = i; light paths are reversible.
  • Plane mirror: image and object are symmetric about the mirror, image distance = object distance, image height = object height; viewing angle = 2 arctan(h / 2D), with D the eye-to-image distance.
  • Refraction: n₁ sin i = n₂ sin r; water 1.33, glass 1.50, diamond 2.42, air 1.00.
  • Total internal reflection: from a denser to a less dense medium, sin C = 1/n; reflected and refracted energies follow the Fresnel equations averaged for natural light.
  • Convex lens: 1/u + 1/v = 1/f, magnification |v/u|; spot size on the screen = D·|s − v| / |v|, lens aperture D = 4 cm.
  • Double slit: d sinθ = kλ, Δx = Lλ/d; intensity = cos²(πd sinθ/λ) times the single-slit envelope (slit width 0.01 mm).
  • Polarization: natural light through one polarizer keeps half; I = I₁ cos²θ, where I₁ is the polarized intensity reaching the analyzer.

Indices are the usual textbook values near sodium yellow; OpenStax lists crown glass at 1.52, this page uses the textbook 1.50. The 4 cm lens aperture, 2.4 cm flame, 0.01 mm slit width and the observer 32 cm from the glass plate are teaching assumptions: they change the picture and spot size, not the image distances or fringe spacing. Rays are drawn segment by segment only to show the order, not the speed of light; the blur of the flame on the screen comes from the spot size and its brightness is only indicative.

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