Physics · Ch 6 — Optics

Angle of Deviation Produced by Prism

6.7.1

Angle of Deviation Produced by Prism

A ray $PQ$ strikes the first refracting face $AB$ of a prism at incidence angle $i_1$ , refracting to $r_1$ as it enters the glass; it crosses the prism as $QR$ , then strikes the second face $AC$ from inside at $r_2$ , refracting out at emergence angle $i_2$ as the ray $RS$ . The deviation contributed at the first face is $d_1=i_1-r_1$ , and at the second face $d_2=i_2-r_2$ ; the total deviation is $d=d_1+d_2=(i_1+i_2)-(r_1+r_2)$ . Because the two normals at the entry and exit points, drawn together with the apex $A$ , complete a quadrilateral containing two right angles, geometry gives $r_1+r_2=A$ , so the deviation simplifies to $\boxed{d=i_1+i_2-A}$ . This shows the deviation depends on: (i) the angle of inciden …

Figure 6.40Prism

What this figure shows. A triangular prism of apex (refracting) angle A is shown, bounded by two polished refracting faces meeting at the apex and a third, ground face forming the base opposite it. The apex angle A, measured between the two refracting faces, is the single geometric parameter (alongside the material's refractive index) that fixes how strong …

Figure 6.41Refraction through prism

What this figure shows. A ray PQ strikes the first refracting face AB of a prism at incidence angle i1, refracting to angle r1 as it enters the glass; it crosses the prism as QR, striking the second face AC from inside at angle r2, and emerges as the ray RS at angle i2 (the angle of emergence). The incident ray PQ and emergent ray RS, extended, meet at a point M, and the angle between them there is the total angle of deviation d; the diagram is the basis for splitting this total deviation into a contribution d1 = i1 - r1 at the first face and d2 = i2 - r2 at the second, which together with the quadril …

Misc Example 6.19Angle of deviation for a 30 degree incidence, 75 degree emergence ray through an equilateral prism

Worked out. A monochromatic ray strikes an equilateral prism (apex angle A = 60 degrees) at incidence angle i1 = 30 degrees and is found to emerge at angle i2 = 75 degrees. Substituting directly into d = i1 + i2 - A gives d = 30 + 75 - 60 = 45 degrees -- a direct, one-line application of the deviation formula once both the incidence and emergence angles are already known from measurement, without needing to separately track the internal refraction angles r1 and r2 at all. …

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