The Foci of Convex Lenses
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
p-467
2025-12-18
33
The positions of the luminous point for which we may determine foci in convex lenses are similar to those considered for concave mirrors. To determine the focus of any point, two rays only are needed. The principal axis or a secondary axis is taken for one of these rays.
- When the Luminous Point is at an Infinite Distance. - In this case the incident rays are parallel, and if we take the index of refraction as,3/2 the focus is very near the center of curvature for a double convex lens, and at twice that distance for a plano-convex lens. This is the principal focus, and its distance from the lens is the focal length of the lens.
- When the Luminous Point is at a Finite Distance More than Twice the Focal Length. - If the path of the ray PA (Fig. 2) is constructed, it will be found to intersect the principal axis at P', between C" and twice the focal length.
- When the Luminous Point is at Twice the Focal Length. -A construction will show that the focus is also at twice the focal length on the other side of the lens.
- When the Luminous Point is at Less than Twice and More than Once the Focal Length. -This is the converse of (b), as is shown in Fig. 492, since if the luminous point is P', its focus will be Р.
- When the Luminous Point is at the Principal Focus. -This is the converse of (a), and the emergent rays will be parallel to the principal axis.
- When the Luminous Point is between the Principal Focus and the Lens.- In this case the rays will emerge as divergent rays, and the focus will be virtual, on the same side of the lens as the luminous point, and farther away from the lens.
Converging lenses render parallel rays converging, increase the convergence of converging rays, and decrease the divergence of diverging rays, or render them parallel or converging.
Demonstration. - Figure 3 shows how the focus of parallel rays can be found by the use of the optical disk.
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