Light & Optics
High SchoolReflection, refraction and lenses
Light is an electromagnetic wave travelling at c = 3.00×10⁸ m·s⁻¹ in vacuum. Geometric optics treats it as rays.
Law of reflection: angle of incidence equals angle of reflection, both measured from the normal.
Refraction (Snell's law): light bends when entering a medium of different optical density, characterised by refractive index n = c/v:
When passing to a less dense medium beyond the critical angle sinθc = n₂/n₁, light undergoes total internal reflection — the principle of optical fibres.
Lens and mirror equation
A converging lens (f > 0) forms real inverted images of distant objects; within the focal length it acts as a magnifier, giving a virtual upright image.
Why the sky is blue and rainbows form
Refractive index depends slightly on wavelength — dispersion. Blue light bends more than red in glass, so a prism spreads white light into a spectrum. In raindrops, refraction + internal reflection + refraction separates sunlight into a rainbow, with red on the outer edge (deviated ~42°) and violet inner (~40°).
The blue sky comes from Rayleigh scattering: air molecules scatter short (blue) wavelengths far more strongly than long (red) ones — scattering ∝ 1/λ⁴. Sunlight's blue is scattered across the whole sky. At sunset, light travels a long slanted path; the blue is scattered away before reaching you, leaving the reds and oranges.
Worked example — image in a converging lens
An object is placed 30 cm from a converging lens of focal length 10 cm. Find the image position, magnification and nature.
- Lens equation:
1/f = 1/v − 1/u. Usingu = −30 cm(object left of lens),f = +10 cm. 1/v = 1/f + 1/u = 1/10 + 1/(−30) = 3/30 − 1/30 = 2/30.- So
v = 30/2 = +15 cm— image is 15 cm on the far side (positive ⟹ real). - Magnification:
m = −v/u = −15/(−30) = −0.5. Negative ⟹ inverted; |m|<1 ⟹ diminished. - Conclusion: a real, inverted, half-size image — exactly how a camera images a distant scene onto its sensor.
Move the object inside the focal length (u = −5 cm) and v turns negative: a virtual, upright, magnified image — the lens now works as a magnifying glass.
Light passes from air (n=1.00) into glass (n=1.50) at 40° incidence. Find the refraction angle.
Snell: 1.00 sin40° = 1.50 sinθ₂, so sinθ₂ = 0.643/1.50 = 0.428, giving θ₂ = 25.4°. Light bends toward the normal entering the denser medium.
What is the critical angle for a glass–air boundary (n_glass = 1.50)?
sinθc = nair/nglass = 1.00/1.50 = 0.667, so θc = 41.8°. Beyond this angle, light inside the glass is totally internally reflected — the basis of fibre-optic communication and diamond's sparkle.
Why does a straw look bent in a glass of water?
Light from the submerged part refracts as it leaves the water into air, bending away from the normal. Your brain assumes light travelled straight, so the underwater portion appears displaced — making the straw look broken at the surface.
Why is the sky blue but the Sun appears yellow/red at sunset?
Rayleigh scattering (∝ 1/λ⁴) scatters blue far more than red, filling the daytime sky with blue. At sunset the light traverses much more atmosphere; nearly all the blue is scattered out of the direct beam, so the Sun's remaining light — dominated by red and orange — reaches your eye.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1Light in air (n=1.0) hits water (n=1.33) at 30 degrees. Find the refraction angle.
- 1.0*sin(30) = 1.33*sin(t2)
- sin(t2) = 0.5/1.33 = 0.376
- t2 = arcsin(0.376)
Example 2An object is 30 cm from a converging lens of focal length 10 cm. Find the image distance.
- 1/f = 1/v + 1/u form: 1/10 = 1/v + 1/30
- 1/v = 1/10 - 1/30 = 3/30 - 1/30 = 2/30
- v = 30/2
Now you try
Work each one out first, then tap to reveal the worked answer.