The big idea: Dip a straw into a glass of water and it looks snapped in half at the surface; a swimming pool looks shallower than it really is. That bending of light as it crosses from one material into another is refraction.
It bends because the light changes speed at the boundary.
The normal is the dashed line drawn at 90° to the surface — every angle is measured from the normal, not from the surface.
New word — refractive index: The refractive index n of a material tells you how much it slows light down.
A bigger n means slower light and more bending. We call a high-n material 'denser' (optically denser).
Vacuum/air ≈ 1.0 · water ≈ 1.3 · glass ≈ 1.5.
Entering the denser, slower glass the ray bends TOWARD the normal: θ₂ (30°) is smaller than θ₁ (50°). The dashed line is the normal — all angles are measured from it.
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Which way does it bend?: Into a denser (slower) medium → bends toward the normal (angle gets smaller).
Into a less-dense (faster) medium → bends away from the normal (angle gets bigger).
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Snell's law links the two angles to the two refractive indices. The data booklet gives it as a set of ratios; the form you actually use rearranges to the line below.
- refractive index of medium 1 (no units)
- refractive index of medium 2 (no units)
- angle of incidence, measured from the normal (°)
- angle of refraction, measured from the normal (°)
Index also fixes the speed: The refractive index also tells you the light's speed in the material: n = c ÷ v.
So a high index means a slow speed. This one is given too.
- refractive index of the medium (no units)
- speed of light in a vacuum, 3.0 × 10⁸ m s⁻¹
- speed of light in the medium (m s⁻¹)
n = c ÷ v. Cover the quantity you want: c on top, n and v underneath. Two side by side → multiply; one above the other → divide.
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Light travels from air (n₁ = 1.0) into glass (n₂ = 1.5), hitting the surface at an angle of incidence of 50° to the normal. Find the angle of refraction in the glass.
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How this is tested — refraction questions split into two jobs:
Paper 1A
- A quick Snell's-law calculation — find an unknown angle or index.
- Sometimes through two layers in a row.
Paper 2
- Predict total internal reflection (TIR) — decide whether light escapes a denser medium or reflects back, using the critical angle.
The classic trap: Measuring an angle from the surface instead of from the normal, or forgetting TIR only happens going denser → less-dense.
Total internal reflection and the critical angle: Going from a denser medium to a less-dense one, the ray bends away from the normal. Make the angle big enough and the refracted ray would need to bend past 90° — it cannot, so all the light reflects back inside. That is total internal reflection (TIR).
The critical angle θc is the incidence angle at which the refraction angle is exactly 90°. Above θc you get TIR.
- critical angle (°) — the incidence angle giving a 90° refraction
- index of the denser medium the light starts in
- index of the less-dense medium it tries to enter
Going from the denser glass toward the less-dense air at a steep angle (60°, past the critical angle), no light escapes — it is all reflected back. This is total internal reflection.
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Light inside a glass block (n₁ = 1.5) meets the boundary with air (n₂ = 1.0). (a) Find the critical angle for this glass–air boundary. (b) A ray inside the same block hits the boundary at 55° to the normal — does it escape into the air, or is it totally internally reflected?
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