Ray Optics and Optical Instruments

9.2.4 Mirror Equation

Relation for image distance $v$, object distance $u$, and focal length $f$:
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
Magnification (m) defined as:
$m = \frac{h'}{h} = -\frac{v}{u}$

9.3 Refraction

Snell's Law:
$\frac{\text{sin} \ i}{\text{sin} \ r} = n<em>{21}$ where $n</em>{21}$ is the refractive index of medium 2 with respect to medium 1.

9.4 Total Internal Reflection

Expression for critical angle:
$\text{sin} \ i<em>c = \frac{n</em>2}{n_1}$.

9.5 Refraction at Spherical Surfaces and by Lenses

Lens Maker's Formula:
$\frac{1}{f} = \frac{(n<em>2 - n</em>1)}{R<em>1} - \frac{(n</em>2 - n<em>1)}{R</em>2}$
for lenses, where $R<em>1$ and $R</em>2$ are radii of curvature.

9.6.1 Microscopes

Formula for magnification (m):
$m = \frac{D}{f} + 1$
where $D$ is the least distance of distinct vision.

9.6.2 Telescopes

Magnifying Power (m):
$m = \frac{f<em>o}{f</em>e}$
for a telescope.