A Course in Phonetics, Fourth edition by Peter Ladefoged

By Peter Ladefoged

The straightforward to appreciate method builds at the fundamentals, starting with technical phrases required for describing speech and transcription symbols ahead of relocating directly to the phonetics of English and different languages.

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The emergent ray, be it reflected or refracted, also has an angular subtense measured from the normal. It will be assumed, unless otherwise stated, that an incident, reflected, or refracted angle is measured from the normal. Read all questions carefully to be sure that angles are defined normal to the surface. Law of Reflection Light that is reflected at an interface leaves the surface traveling in the opposite direction (Figure 2-5). For any incident angle, the angle of reflection may be calculated using the Law of Reflection: The angle of incidence is equal to the angle of reflection.

As shown, from the normal to the surface is a 90° angle. The internal angles that the ray makes with these normals are part of each right angle. The remainder of the right angles are contained within the outlined triangle angles and are Prisms represented by (90°- &χ) and (90°- QtfUsing the simple geometric fact that the sum of the internal angles of a triangle is equal to 180°, the relationship between the internal angles and the apical angle is easily derived: 47 B / Λ / (90°- &i) + (90°- θ 2 ) + γ = 180° I V \ ^{iimiiiiiiiiiiiTiiiiiiniiiiiiiiiiniiiinFiiiiiiiiiiiiftiiiitf^ | Combining terms and solving for γ yield 1 8 0 β - θ * 1 - θ 2 + γ =180° ftwWWWWWWW γ=θ·1 + θ2 (3-2) Figure 3-3.

Equations/Concepts (2-5) Snell'sLaw Refraction through parallel-sided plate Unknown Lateral displacement Known Glass plate thickness: t = 15cm Incident angle = 45° Start with a diagram of a ray being refracted through a parallel sided plate (Figure 2-15, for example), extend the incident ray through the plate, and draw a line perpendicular from the incident to the emergent ray. In Figure 2-19b, several angles and triangles are labeled. The angle that encompasses both triangles is labeled θ^, the refracted angle in the lower striped triangle is labeled &\, and the angle in the shaded triangle is the difference between these two angles or {θ^—G'^} as indicated.

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