Chapter 23 Mirrors and Lenses

23.1 Flat Mirrors

• Figure 23.1 and 2

• Definition of terms: Object distance (p), image distance (q)

• In any cases, images are formed at the point at which rays of light actually intersect or at which they appear to originate.

• All the rays that leave a given point on the object, no matter what angle they have when they strike the mirror, appear to originate from a corresponding point on the image behind the mirror.

• Lateral magnification is defined as

M =

where h is the image height and h^’is the object height.

• The image from a flat mirror is

(1) as far behind the mirror as the object is in front (p = q).

(2) unmagnified, virtual, and upright.

• A virtual image is one from which all the rays of light do not actually emanate from the image, but only appear to do so.

• A real image is one from which all the rays of light are actually emanate from the image (can be projected on a screen).

• Examples

23.2 Images Formed by Spherical Mirrors

• A spherical mirror has the shape of a section from the surface of a sphere.

• The principal axis of a mirror is a straight line drawn through the center of curvature and the middle of the mirror’s surface.

• The radius of curvature R of the mirror is the distance from the center of curvature to the mirror.

• Concave vs. convex mirrors (Figure 23.6 and Figure 23.10)

• Incident rays parallel to the principle axis converge to (diverge from) the focal point after being reflected from the concave (convex) mirror.

• The distance between the focal point and the middle of the mirror is the focal length f of the mirror.

|f| = |R|

• f is + for a concave mirror, f is – for a convex mirror.

• Mirror equation (23.4)

+ =

where f = the focal length of the mirror, p = the object distance, and q = the image distance.

• Magnification equation (23.2)

M = = -

23.3 Convex Mirrors and Sign Conventions

• Figure 23.12 (a) (b)

Ray Tracing for a Concave Mirror

Ray 1. This ray is initially parallel to the principal axis and therefore passes through the focal point F after reflection from the mirror.

Ray 2. This ray passes through the focal point F and is reflected parallel to the principal axis. Ray 2 is analogous to ray 1, except the directions of the incident and reflected rays are interchanged.

Ray 3. This ray travels along a line that passes through the center of curvature C and follows a radius of the spherical mirror; as a result, the ray strikes the mirror perpendicularly and reflects back on itself.

• Example

• Figure 23.12

Ray Tracing for a Convex Mirror

Ray 1. This ray is initially parallel to the principal axis and therefore appears to originate from the focal point F after reflection from the mirror.

Ray 2. This ray heads toward the focal point F, emerging parallel to the principal axis after reflection. Ray 2 is analogous to ray 1, except the directions of the incident and reflected rays are interchanged.

Ray 3. This ray travels toward the center of curvature C; as a result, the ray strikes the mirror perpendicularly and reflects back on itself.

• Example

Summary of Sign Convention for Spherical Mirrors (Table 23.1)

Focal length

f is + (-) for a concave (convex) mirror.

Object distance

p is + (-) if the object is in front of (behind) the mirror.

Image distance

q is + (-) if the image is in front of (behind) the mirror.

Magnification

M is + (-) for an image that is upright (inverted) with respect to the object.

23.4 Images Formed by Refraction (Skip)

23.5 Atmospheric Refraction (Reading Assignment)

23.6 Thin Lenses

• With converging lenses, rays that are parallel to the principal axis are focused to a point on the axis by the lens. This point is called the focal point of the lens, and its distance from the lens is the focal length f. (Figure 23.23 (a))

• With diverging lenses, paraxial rays appear to originate from its focal point after passing through the lens. (Figure 23.23 (b))

• Figure 23.26

Ray Tracing for Converging (Diverging) Lenses

Ray 1. This ray is initially parallel to the principal axis. In passing through a converging (diverging) lens, the ray is refracted toward (away from) the axis and travels through (appears to have originated from) the focal point on the right (left) side of the lens.

Ray 2. This ray first passes through the focal point on the left and then is refracted by the lens in such a way that it leaves traveling parallel to the axis. (This ray leaves the object and moves toward the focal point on the right of the lens. Before reaching the focal point, however, the ray is refracted by the lens so as to exit parallel to the axis.)

Ray 3. This ray travels directly through the center of the thin lens without any appreciable bending. (the same in both cases)