echoesof.science · Ages 15–16
Light: rays, reflection, dispersion and the electromagnetic spectrum
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Light is an electromagnetic wave. In a vacuum it travels at c = 3.00 × 10⁸ m/s (only slightly slower in air), and like any wave it obeys c = f·λ. Visible light has wavelengths from about 400 nm to 750 nm: red has the longest wavelength and lowest frequency, violet the shortest wavelength and highest frequency.
In geometric optics light is modelled as rays travelling in straight lines, which change direction at a mirror or at the boundary between two materials. At a mirror, the angle of reflection equals the angle of incidence, both measured from the normal. A surface that is smooth compared with the wavelength gives a sharp image; a rough surface scatters light in all directions (diffuse reflection).
White light is a fairly uniform mixture of all visible wavelengths. Because a material's refractive index depends on wavelength, each colour refracts by a different amount: this is dispersion. In glass and water the index is higher for shorter wavelengths, so violet bends more than red. A rainbow forms when sunlight refracts entering a raindrop, reflects off the back and refracts again on leaving.
Experiment: Test the law of reflection
- Draw a straight line across the paper and stand the mirror on it, reflecting side along the line.
- Draw the normal: a line at 90° to the mirror line, in the middle of the page.
- Shine a narrow ray along the paper so it hits the mirror exactly where the normal meets it.
- Mark the incoming and reflected rays with two pencil dots each, then remove the mirror and draw the rays with a ruler.
- Measure the angle of incidence i and the angle of reflection r from the normal.
- Repeat for at least five angles (for example 15°, 30°, 45°, 60°, 75°) and plot r against i.
| Angle of incidence i (°) | Angle of reflection r (°) | Difference r − i (°) |
|---|---|---|
| 15 | ||
| 30 | ||
| 45 | ||
| 60 | ||
| 75 |
Questions
State the law of reflection and draw a labelled ray diagram (incident ray, reflected ray, normal, i and r).
Calculate the frequency of red light with λ = 700 nm.
Explain, using the idea of refractive index, why a prism spreads white light into a spectrum.
Your results: does r = i? Give two sources of error in your experiment and how to reduce them.
Sources for every fact on this sheet: echoesof.science/school/light/sources/