MYP Physics · topic MYP-12.03
Colour, spectra, and dispersion
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
A prism separates colours but preserves frequencies
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. White light enters glass from air at 30° to the normal. The material's measured refractive indices at several vacuum wavelengths are supplied. Air has index 1.00 and c = 3.0×10⁸ m s⁻¹. Treat the colours independently and use Snell's law. Supplied data (Vacuum wavelength / nm; Refractive index): (400, 1.54), (550, 1.52), (700, 1.5). (a) Compare the refracted angles, glass speeds and glass wavelengths for 400 nm and 700 nm light. [3 marks] (b) Explain why recombining the spectrum can produce white light and distinguish this from mixing coloured paints. [3 marks]
Glass dispersion
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Refractive index
Horizontal axis (x): Vacuum wavelength / nm
Read the exact data as a table
| Vacuum wavelength / nm | Refractive index |
|---|---|
| 400 | 1.54 |
| 550 | 1.52 |
| 700 | 1.5 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Show a hint
Begin with part (a): Compare the refracted angles, glass speeds and glass wavelengths for 400 nm and 700 nm light.
Reveal the worked solution
- Snell's law gives sin r = sin30°/n. The blue/violet value is asin(0.5/1.54)≈18.9° and the red value is asin(0.5/1.50)≈19.5°.
- Speeds are c/n, about 1.95×10⁸ and 2.0×10⁸ m s⁻¹. Higher index gives greater bending toward the normal on entry.
- Frequency is unchanged at entry, so λglass = λvacuum/n, giving about 260 and 467 nm. Dispersion separates directions because n depends on wavelength.
- A second appropriately oriented prism or lens arrangement can recombine the separated spectral components into the original white-light mixture.
- The first prism separates pre-existing frequencies; it does not manufacture colours or convert red photons into blue ones.
- Coloured pigments absorb and scatter different bands, so pigment mixing is subtractive and does not follow the same colour rules as adding light beams.
Answer (a) 400 nm: r≈18.9°, v≈1.95×10⁸ m s⁻¹, λglass≈260 nm; 700 nm: r≈19.5°, v=2.0×10⁸ m s⁻¹, λglass≈467 nm. (b) Light addition combines spectral components; paints remove selected components through absorption.
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.