IMAGES, SURFACES, AND LENSES

I. Our goal is to understand how images are formed with optical elements so that optical systems may be designed.

II. Plane Mirrors

A. The object and image are the same distance from the mirror.

B. The magnification is one and the image is virtual and upright.

C. There is left-right reversal.

III. Spherical Mirrors

A. For a spherical mirror the magnification is given by: m = -(i/p)

B. The "mirror equation" is: (1/p) + (1/i) = 1/f = 2/R

1. This is obtained using the law of reflection, geometrical arguments, and the small angle approximation

3. This is good for paraxial rays.

IV. Sign Conventions

A. If the object is on the same side of the surface as the incident light, then the object distance (p) is positive.

B. If the image is on the same side of the surface as the reflected (or refracted) light, then the image distance (i) is positive.

C. If the center of curvature is on the same side of the surface as the reflected (or refracted) light, then the radius of curvature    (R) is positive

V. For a single spherically-shaped refracting surface, we can apply the law of refraction, geomertical arguments, and the small angle approximation to get:

n1/p + n2/i = (n2 - n1)/R          and             m = - n1i/n2p

VI. If we have a thick lens and two surfaces, we have to apply the above equation twice using the image formed by the first surface as the object for the second surface.

VII. What approximation do we make using the procedure in VI to get our thin lens equation?

1/p + 1/i = [(n2/n1) - 1][(1/R1) - (1/R2)]

A. If we use the lens maker's equation

1/f = [(n2/n1) - 1][(1/R1) - (1/R2)]

we get the thin lens equation:

1/p + 1/i = 1/f         and         m = - i/p

EXAMPLES

Text Ch. 35: Problems 16, 20, 37