Lesson 4 of 6 · Reflection and refraction
Follow light at a boundary
8 minute lesson · 3 checks along the way
Your goal for this lessonPredict a simple reflected or transmitted path while distinguishing direction changes, wavelength changes, and color separation.
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Draw the reference line first
When light encounters a boundary, some may return into the original by . For a smooth surface, the reflected ray makes the same angle to the normal as the incoming ray. The normal is an imaginary line perpendicular to the surface at the point of contact. Measuring angles from the surface instead of the normal is a common source of misleading diagrams and incorrect comparisons.
A rough surface can scatter reflected light in many directions because small areas have different orientations. That is why an illuminated wall is visible from many positions while a mirror forms a more organized image. Reflection does not necessarily mean every returns: a material can also transmit or absorb part of the incoming light. The fractions depend on , material, and the geometry of the encounter.
A transmitted wave can change its path
Light propagating through a transparent material generally has a different speed from light in vacuum. The , n, describes the ratio c divided by that speed. Crossing an ordinary stationary boundary at an oblique angle can therefore bend the transmitted path: . Entering a higher-index material bends the ray toward the normal; entering a lower-index material bends it away when a transmitted ray exists.
At incidence, the transmitted ray continues straight even though its speed and wavelength can change. In this stationary, ordinary refraction example, stays the same across the boundary. Since speed equals frequency times wavelength, a lower speed means a shorter wavelength in the material. This is not the same as changing the light source to a lower-frequency emitter, and it does not require calling the light a new visible color.
Check 1 of 3
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Work through a decision
Check two labels on an optical diagram
A hypothetical diagram shows a ray meeting a smooth boundary at 30 degrees to the normal. Its reflected ray should also make 30 degrees to that normal, on the outgoing side. A label claiming 60 degrees to the normal has mixed up the reference lines. Correct the geometry before interpreting the apparatus. This exercise uses a diagram; it requires neither a laser nor looking at the Sun.
The transmitted part enters a material whose refractive index is 1.5. Using a rounded c of 300,000 kilometers per second gives a speed of 200,000 kilometers per second. At unchanged frequency, its wavelength becomes two-thirds of the vacuum value. A second label claiming that both wavelength and frequency fall by the same factor is inconsistent with the stated speed and the stationary boundary conditions.
Check 2 of 3
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Separate colors and gather images
Refractive index often varies with wavelength. A prism can consequently send different components of white light in different directions, producing . Water droplets combine refraction, internal reflection, and dispersion to form an ordinary rainbow. The droplets sort light already present in sunlight; they do not manufacture an entirely new set of visible frequencies. A rainbow photograph records the resulting viewing geometry, not a physical colored bridge attached to the ground.
Lenses use shaped transparent surfaces to redirect rays by refraction; curved mirrors gather and redirect them by reflection. Telescope designers choose materials, coatings, and shapes for the wavelengths they need to measure. A neat ray diagram is a powerful starting point, but it leaves out the wave spreading that occurs at finite openings. That next limitation explains why even an accurately focused telescope cannot separate arbitrarily close sources.
Atlantis and Endeavour at Kennedy Space Center in September 2008, beneath a visible rainbow. NASA photographer Jack Pfaller recorded this conventional aerial photograph; the full source frame is retained. The rainbow is an optical effect involving sunlight and droplets, not colored material attached to either launch pad.
Look closely
Locate the rainbow above the pads. Does its apparent position establish that its colored light originates from the Shuttle hardware?
See what to notice
No. The apparent alignment belongs to the observer’s view. Refraction, internal reflection, and wavelength-dependent dispersion of sunlight in droplets explain an ordinary rainbow. The photograph does not provide a ray diagram or an independent droplet-size measurement.
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Put it together
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