1. Lecture 14 Mirrors Chapter 23.1  23.3 Outline Flat Mirrors Spherical Concave Mirrors Spherical Convex Mirrors

2. Flat Mirrors Source of light is placed at point O at a distance p from a flat mirror. Point I is the image of point O. q is the image distance. Image is formed at the ray intersection point, either real or apparent. Images seen in flat mirrors are always virtual images. pq

3. Images in Flat Mirrors To find out where an image is formed, follow at least two rays reflected from the mirror. Triangles PQR and P′QR are identical  PQ = P′Q The distance between the image and the mirror is the same as the distance between the object and the mirror, but they are located at different sides of the mirror.

4. Magnification Lateral magnification M is defined as follows: image height h′ M ≡  =  object height h M = 1 for flat mirrors. The image in a flat mirror is unmagnified, virtual, and upright and have an apparent left-right reversal.

5. Spherical Mirrors A spherical mirror is a reflecting segment of a sphere. A concave mirror is a spherical mirror with a reflecting inner, concave surface.

6. Spherical Mirrors The image I of the object O is real. The image is sharp when the diverging rays from the object make small angles with the principal axis. When these angles are large, the reflected rays intersect at different points and form a blurry image. This phenomenon is called spherical aberration.

7. Image Formation in Concave Mirrors tan  = h/p =  h'/q M = h'/h =  q/p tan  = h/(p  R) tan  =  h'/(R  q) h' R  q q  =  =  h p  R p  1 1 2  +  =  p q R Mirror equation

8. Images in Concave Mirrors When the object is far away from the mirror, the image point is roughly halfway between the center of curvature and the center of the mirror. In this case incoming rays are nearly parallel to each other, the image point is called the focal point, and the image distance is called the focal length (f = R/2). 1 1 1  +  =  p q f

9. Image Types A real image is formed when light rays pass through and diverge from the image point. A virtual image is formed when light rays do not pass through the image point but appear to diverge from that point.

10. Convex Mirrors Problem: a candle is 49 cm from a convex mirror of 70 cm radius. Find the image distance and magnification. 1 1 2  +  =  p q R 1 1 2  =   +  q p R q =  20.4 cmM =  p/q = 0.417R =  70 cm

11. Sign Convention

13. Summary Flat mirrors form virtual and unmagnified images. Spherical mirrors form both real and virtual images. Focal point of a spherical mirror is a point where parallel incoming rays intersect after reflection. The mirror equation connects the object distance, the image distance, the radius of the mirror curvature.