A concave mirror has a 4-m radius of curvature. This mirror will focus distant objects at a location that is approximately:

Question

A concave mirror has a 4-m radius of curvature.  This mirror will focus distant objects at a location that is approximately:

Quizplus · Accepted Answer

11ecba2d_131a_2da1_a3bf_27fed621c1e8_MD0008_00 Spherical mirrors are a specific class of curved reflective surfaces shaped like a portion of a sphere. Spherical mirrors are further classified as concave (converging) or convex (diverging). The reflective surface of concave (converging) mirrors curves inward, away from the object and incident (incoming) light. Conversely, the reflective surface of convex (diverging) mirrors curves outward, toward the object and incident light. The focal length (f) of a concave mirror is the distance in front of the mirror at which reflected light rays converge to form an image. Concave mirrors will form an inverted, real image when the reflected object is located outside of the focal length, but when the object is placed inside the focal length of a concave mirror, an upright, virtual image is formed. In contrast, convex mirrors always form an upright, virtual image. Ignoring spherical aberrations, the focal length of a spherical mirror is equal to half the radius of curvature (r) (Choice A), where r is the distance between the midpoint of the mirror surface and the center of the imaginary sphere of which the mirror surface is only a portion: 11ecba2d_131a_2da2_a3bf_434fb2bf692e_MD0008_00 The equation for focal length is identical for both convex and concave mirrors. Consequently, a concave mirror and a convex mirror with the same radius of curvature will have identical focal length magnitudes. However, the point of focus is positioned in front of a concave mirror and behind a convex mirror (Choices B and D). This question introduces a concave mirror with a radius of curvature of 4 m. The focal length of the concave mirror may be calculated as: 11ecba2d_131a_2da3_a3bf_3d0ed51577b3_MD0008_00 Because concave mirrors converge distant objects to form real, inverted images beyond the focal length of the mirror, this concave mirror will focus the light rays emanating from a distant object at a location that is at least 2 m in front of the mirror. Educational objective: Concave (converging) spherical mirrors create real, inverted images of objects placed outside of mirror focal length. The focal length of a concave spherical mirror is half the radius of curvature and is positioned in front of the mirror.

A Concave Mirror Has a 4-M Radius of Curvature