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4.1.1.       Reflection of Light & Mirrors   <CJ chap 25  >

4.1.1.1. Discussion

4.1.1.1.1.     Flat Mirrors

4.1.1.1.1.1. Law of reflection is that the angle (to the normal) of reflection is equal to the angle of incidence

4.1.1.1.1.2. The left and right handiness is reversed in a mirror (eg with handwriting)

4.1.1.1.1.3. A reflected image is as far behind a mirror as the object is in front and is upright

4.1.1.1.2.      Spherical Mirrors

4.1.1.1.2.1. Using a normal to the surface, one can show that the focal length is half of the radius of the mirror

4.1.1.1.2.2. The focal length is here defined as the position of a focused image from infinity

4.1.1.1.2.3. Likewise for a a reflection in either a convex or concave mirror focal length is half the radius

4.1.1.1.2.4. Note that not all rays from infinity focus exactly there but only those near the center

4.1.1.1.2.5. Note ray tracing to form an image of an object in convex & concave mirrors (Example)

4.1.1.1.2.6. A concave mirror gives enlarged, upright, virtual images in front of the mirror

4.1.1.1.2.7. A convex mirror gives diminished, upright, virtual image behind the mirror

4.1.1.2. Mathematical

4.1.1.2.1.     Law of reflection is that the angle of incidence equals the angle of reflection q_i=q_r

4.1.1.2.2.     The focal length of both convex and concave mirrors is given by f = R/2 where R is the radius

4.1.1.2.3.     Let d_o and d_i be the distances of the object and image to the mirror then 1/d_o + 1/d_i = 1/f

4.1.1.2.4.     And the magnification is m = - d_i /d_o (if negative then image is inverted, if positive then upright)

4.1.1.3. Advanced