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Additional resources for Robin Hartshorne's Algebraic Geometry Solutions. Chapter II Section 7, Projective Morphisms
Example text
REFRACTION of the incident ray. 5, the refracted ray BC has been deviated toward the perpendicular by one sector relative to the incident ray AB. Since this is the angle of refraction, it is labeled ρ. When the diagram is interpreted in reverse, light inside the glass is directed against the surface along CB. The refracted ray in air must be BA, since ray diagrams are reversible. Thus, the light is deviated away from the perpendicular by one sector, again labeled ρ. In this case, the inclination φ of the incident ray CB is two sectors, so the angle of refraction is half the inclination of the incident ray.
In general, the closer a point source is to a given aperture, the larger the apical angle of the cone of rays passing through the aperture. Intuitively, the larger the apical angle of a ray cone, the more divergent the rays in the cone. Now, the DIVERGENCE 23 divergence of two rays is naturally defined as the angle between them. But when we try to apply this definition of divergence to a cone of rays, there is the problem that the cone consists of a multiplicity of rays and there are different angles between different rays in the cone.
LOOKING THROUGH A LENS Blurring There is a surprising difference between projection of images by a convex lens and observation of objects through the lens. Images projected by a convex lens onto a surface are clear only when the surface is in the vicinity of the convergence points. In contrast, if the eye observes an object from this region, the object appears badly blurred. But if the eye moves closer to the lens than the convergence points, or farther away, the object is seen more clearly. Why?