Reflection & Refraction

Light bends because it changes speed. The rest of what happens at a boundary follows from that, including the angle past which light cannot leave.

35 min4 checkpoints9 simulation tasks

A straw in a glass of water seems to snap at the surface. Where light meets a new clear material, some of it comes back and the rest bends, because it changes speed.

Practice

A ray strikes a flat pond at 30° to the water's surface. What is its angle of incidence?

At the boundary

Try it

Light in air meets crown glass. Run it, then tilt the incoming ray until the ray inside the glass travels at 30° from the normal.

GoalThe ray inside the glass at 30° from the normal.

589 nm: rays drawn at their own colourwavefront distancenormal, boundary, arcs (apparatus)

Angle of incidence

Measured from the NORMAL: the dashed line at right angles to the surface.

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Three things happen at the boundary at once. A reflected ray leaves at the angle the light arrived, as at every boundary, mirror or not: at 40° it carries 4.8% of the power, a shop window's faint ghost of you. A refracted ray goes on, bent toward the normal. And the crests bunch up: the wave is shorter in glass.

The rule

Both angles are measured from the normal, and they obey one rule:

n_1 \sin\theta_1 = n_2 \sin\theta_2

$n$ is the refractive index of a material, and it is a statement about speed:

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

Crown glass has $n = 1.52$ , so light travels through it at about two-thirds of $c$ . The bigger $n$ , the slower the light, and the harder the ray bends.

Try it

The light still arrives at 40°. Change the second material's index $n_2$ until the ray bends to about 15° from the normal.

GoalThe ray inside at about 15° from the normal.

589 nm: rays drawn at their own colourwavefront distancenormal, boundary, arcs (apparatus)

n₂

An invented medium: one number, no dispersion curve, so every colour bends alike.

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Predict

A beam of red light passes from air into a block of glass. Which of its properties change at the surface?

Try it

Set the wavelength in air so that, inside the glass, the wave is 400 nm long.

GoalThe wave 400 nm long inside the glass.

500 nm: rays drawn at their own colourwavefront distancenormal, boundary, arcs (apparatus)

Wavelength in vacuum

The colour every readout follows. Rays are drawn at this wavelength's own colour.

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When the exit closes

From the bottom of a pool, the underside of the surface can look like a mirror. Run the light the other way, from glass out into air, and it bends away from the normal.

Try it

Tilt the ray further from the normal until the ray leaving the glass lies almost flat along the surface.

GoalThe refracted ray almost flat along the surface.

589 nm: rays drawn at their own colourwavefront distancenormal, boundary, arcs (apparatus)

Angle of incidence

Measured from the NORMAL: the dashed line at right angles to the surface.

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Past 41.2° there is no outgoing ray at all. Set $\theta_2 = 90°$ in Snell's law to find this critical angle:

\theta_c = \arcsin\!\left(\frac{n_2}{n_1}\right)

Beyond it Snell's law would need $\sin\theta_2 > 1$ , so all the light comes back. This is total internal reflection, the most efficient mirror there is, with no coating and no absorption. Optical fibres carry calls under oceans this way.

Try it

Light inside a diamond heads out into air. Raise the angle a degree at a time until none of it gets out.

GoalNone of the light gets out of the diamond.

589 nm: rays drawn at their own colourwavefront distancenormal, boundary, arcs (apparatus)

Angle of incidence

Measured from the NORMAL: the dashed line at right angles to the surface.

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Practice

You want to build a periscope with no mirrors in it, using total internal reflection inside glass prisms. Which surface should the light hit for the trick to work?

Why a prism makes a rainbow

Refractive index is not one number per material. It depends on wavelength, always a little and in glass enough to see. This dispersion is why raindrops and cut crystal throw colour.

Try it

Light enters flint glass at 60°. Slide the wavelength and find the colour that bends closest to the normal.

GoalThe colour that bends closest to the normal.

700 nm: rays drawn at their own colourwavefront distancenormal, boundary, arcs (apparatus)

Wavelength in vacuum

The colour every readout follows. Rays are drawn at this wavelength's own colour.

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Try it

White light inside flint glass heads out into air. Raise the angle until blue light, at 450 nm, is trapped while red still gets out.

GoalBlue light (450 nm) trapped, while red still gets out.

380–780 nm: every ray at its own colour, crests at 450 nmwavefront distancenormal, boundary, arcs (apparatus)

Angle of incidence

Measured from the NORMAL: the dashed line at right angles to the surface.

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Practice

In that last setting, flint glass into air near the critical angle, the light that escapes fans out across several degrees of colour. What does the reflected beam do?

Making a boundary

Try it

Light in a material with $n_1 = 1.33$ meets a second material at 40°. Set its index $n_2$ so the ray goes straight on, with nothing reflected.

GoalThe ray goes straight on, with no reflection.

589 nm: rays drawn at their own colourwavefront distancenormal, boundary, arcs (apparatus)

n₂

An invented medium: one number, no dispersion curve, so every colour bends alike.

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Try it

Both sides now have $n = 1.50$ , so there is no boundary. Lower $n_2$ a hundredth at a time until light at 70° can no longer get out.

GoalLight at 70° can no longer get out.

589 nm: rays drawn at their own colourwavefront distancenormal, boundary, arcs (apparatus)

n₂

An invented medium: one number, no dispersion curve, so every colour bends alike.

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The ticks along each ray hold the ray and wave pictures together: the ray is where the light goes, and the spacing of the ticks is the wave that decides where that is.

What comes next

A single flat boundary bends a ray once. Curve the boundary, or stack two of them, and the same rule starts to bring rays back together at a point. That is a lens, and it is the whole of image formation.

Ideas this lesson took on

Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.

“The angle of incidence is measured from the surface”
“Glass slows light down by absorbing some of it”
“The frequency of light changes when it enters glass”
“Total internal reflection happens when light hits a denser material”

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Research behind this lesson

Ambrose et al. 1999: University students who had studied physical optics at introductory level and beyond often could not account for the pattern light makes on a screen after a single or double slit; many did not know whether to apply geometrical or physical optics to a given situation and inappropriately combined elements of both, and some difficulties were serious enough to preclude even a qualitative wave model for light.
Galili & Hazan 2000: High-school students and preservice teachers were probed on light and vision before and after conventional instruction; their knowledge afterwards was best described as a hierarchy of alternative facets and schemes rather than a single coherent model, with the pre-instruction ideas largely surviving.
Kaewkhong et al. 2010: Two diagnostic questions given to 220 year-11 students after instruction found persistent errors about the direction light propagates and how it refracts at an interface; only 22% could use a ray diagram qualitatively to locate an image, and just one student of the 220 identified the image position with sound reasoning.
Wosilait et al. 1998: Students who could state that light travels in straight lines frequently could not apply a ray model to predict what appears on a screen; a tutorial built directly on those documented difficulties produced substantially better performance than the standard instruction it replaced.

Reflection & Refraction

Introduction

A ray strikes a flat pond at 30° to the water's surface. What is its angle of incidence?

At the boundary#