lesson
Direction changes depend on the boundary geometry
1 · Learn
Refraction occurs when a wave changes speed between media and can change direction at a boundary. A ray entering along the normal need not change direction even though its speed changes. Angles are measured from the normal, not the surface.
A ray diagram is a model of propagation. Draw the normal first and distinguish incident, reflected and refracted rays; do not aim bright light or lasers at eyes.
2 · Worked example
A ray crossing into a slower medium obliquely bends towards the normal in the usual simple model. Along the normal, no directional bend is required.
3 · Your turn
From which line are incidence and refraction angles measured?
Check your answer
The normal, perpendicular to the boundary.
4 · Apply your learning
Annotate a supplied ray diagram and explain why measuring from the surface gives the complementary angle.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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