Refraction, total internal reflection, optical fibres and lenses
8 min read · about 1 h 20 min with practice3 quick checks≈1% of the testCore: Core: tested on most papers
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Refraction is a short topic that pays reliable marks: a Snell’s law or critical-angle calculation, an optical-fibre explanation and, on some boards, a thin-lens calculation. Marks go on method, not physics: angles measured from the wrong line, the wrong index on top, or mixed lens sign conventions.
By the end you’ll be able to
Use n = c/v and Snell’s law n₁ sin θ₁ = n₂ sin θ₂
Derive and use the critical angle sin θc = n₂/n₁ and explain total internal reflection
Explain step-index optical fibres, the role of cladding, and modal and material dispersion (pulse broadening)
Use the thin-lens equation 1/u + 1/v = 1/f, magnification and lens power in dioptres; draw ray diagrams
Describe how refraction explains image formation in cameras and the eye
What the exam asks
Calculate with n=c/v and Snell’s law at any boundary, not just air and glass.
Decide whether a ray is totally internally reflected, usually after a first refraction.
Explain how a step-index fibre works and how absorption and dispersion limit data rates. AQA often makes this a 6-mark extended response.
Lenses (Edexcel 9PH0, CCEA, OCR B, AQA Astrophysics): ray diagrams, the lens equation, magnification and power.
Practical: plot sini against sinr to find , or against to find .
vii.Check your understanding
3 questions on refraction, total internal reflection, optical fibres and lenses. Every option is explained once you answer.
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PromptCard 1 of 3
Define absolute refractive index.
n
1/v
1/u
f
Core ideas
Refractive index and Snell’s law
The absolute refractive index of a material compares the speed of light in a vacuum with its speed in the material:
n=vc
n has no unit, and n≥1 (take air as 1.00). At a boundary the frequency does not change. The speed and the wavelength both fall by the factor n as light enters a medium with a higher refractive index. Snell’s law:
n1sinθ1=n2sinθ2
Both angles are measured from the normal. Light entering a medium with a higher n bends towards the normal.
Critical angle and total internal reflection
When light travels from a higher n1 towards a lower n2, the angle of refraction reaches 90° at the critical angle θc:
sinθc=n1n2(into air: sinC=n1)
Total internal reflection (TIR) needs both conditions:
Light travels from a higher to a lower refractive index.
The angle of incidence is greater than the critical angle.
Above θcall the light is reflected, unlike ordinary partial reflection. Typical values: glass (1.50) to air 41.8°; water (1.33) to air 48.8°; glass (1.52) to water 61.0°; fibre core (1.48) to cladding (1.46) 80.6°.
Step-index optical fibres
A glass core is surrounded by cladding of slightly lower refractive index, and light meeting the boundary above the critical angle is totally internally reflected all along the fibre. The cladding has three jobs, each worth a mark: its lower index allows TIR, it protects the core from scratches that would let light escape, and it prevents crosstalk between neighbouring fibres.
Effect
Cause
Consequence
Reduce it by
Absorption
Glass absorbs signal energy
Amplitude falls
Pure glass; regenerators
Modal dispersion
Rays at different angles travel different path lengths
Pulse broadening
Narrow (monomode) core; cladding n closer to core n
Material dispersion
n depends on wavelength, so wavelengths travel at different speeds
Pulse broadening
Monochromatic source (laser)
Broadened pulses overlap and cannot be told apart, which limits the bit rate and the distance before regeneration. The axial ray takes t0=Ln1/c; the critical-angle ray travels the longest path, L/sinθc, so
Δt=cLn1(n2n1−1)
Thin lenses
A converging lens brings parallel rays to a real principal focus F, a distance f away; a diverging lens spreads them as if from a virtual focus. PowerP=1/f is in dioptres (D = m⁻¹) with f in metres: positive for converging, negative for diverging, and P=P1+P2 for thin lenses in contact.
Ray diagrams use two of three rays: parallel to the axis → through F (or away from F for a diverging lens); through the optical centre → undeviated; through F → parallel to the axis.
With the real-is-positive convention (Edexcel 9PH0, CCEA, AQA Astrophysics):
u1+v1=f1,m=object heightimage height=uv
A negative v means a virtual image on the same side as the object. Real images are inverted and can be caught on a screen. Virtual images are upright.
For a converging lens: u>2f gives a real, inverted, diminished image (camera, eye); f<u<2f gives a real, inverted, magnified image (projector); u<f gives a virtual, upright, magnified image (magnifying glass).
In the eye, the lens-to-retina distance is fixed, so the ciliary muscles change the lens’s shape and power to focus (accommodation). A camera moves its lens instead. Short sight is corrected with a diverging lens and long sight with a converging lens.
Worked examples
Exam technique
Draw the normal first and measure every angle from it.
“Does it escape?” routine: refract at the first face, use geometry for the next angle (perpendicular faces give 90∘−r), find θc, then state the comparison. The last mark is for the reasoned conclusion.
In sinθc=n2/n1 the larger index goes on the bottom. A calculator error means the ratio is upside down.
Fibre explanations: write cause → pulse broadening → overlap → remedy. Those words earn marks.
Lenses: convert to metres before finding power. “Describe the image” needs all three properties: real/virtual, inverted/upright, magnified/diminished.
Graphs: sini against sinr has gradient n and passes through the origin. For 1/v against 1/u (real is positive), both intercepts equal .
Common mistakes
Quick recap
n=c/v. The frequency is unchanged at a boundary; speed and wavelength both fall by the factor n.
n1sinθ1=n2sinθ2, with angles measured from the normal.
sinθc=n2/n1. TIR needs light going from higher to lower an angle of incidence .
Cladding has a lower n (so TIR happens), protects the core and prevents crosstalk.
Modal dispersion (paths) and material dispersion (wavelengths) broaden pulses; absorption reduces amplitude.
Δt=cLn1( for the axial ray against the critical-angle ray.
Lenses: u1+v1 with real is positive (OCR B uses ), , and in dioptres with in metres.