25.1 The Ray Aspect of Light

A straight line that originates at some point is called a ray.
The part of optics dealing with the ray aspect of light is called geometric optics.
Light can travel in three ways from a source to another location: (1) directly from the source through empty space; (2) through various media; (3) after being reflected from a mirror.

25.2 The Law of Reflection

The changing of a light ray’s direction when it passes through variations in matter is called refraction.
The speed of light in vacuum $c = 2.99792458 \times 10^{8} m/s \approx 3.00 \times 10^{8} m/s .$
Index of refraction $n = \frac{c}{v}$ , where $v$ is the speed of light in the material, $c$ is the speed of light in vacuum, and $n$ is the index of refraction.
Snell’s law, the law of refraction, is stated in equation form as $n_{1} sin θ_{1} = n_{2} sin θ_{2}$ .

The incident angle that produces an angle of refraction of $90º$ is called critical angle.
Total internal reflection is a phenomenon that occurs at the boundary between two mediums, such that if the incident angle in the first medium is greater than the critical angle, then all the light is reflected back into that medium.
Fiber optics involves the transmission of light down fibers of plastic or glass, applying the principle of total internal reflection.
Endoscopes are used to explore the body through various orifices or minor incisions, based on the transmission of light through optical fibers.
Cladding prevents light from being transmitted between fibers in a bundle.
Diamonds sparkle due to total internal reflection coupled with a large index of refraction.

The spreading of white light into its full spectrum of wavelengths is called dispersion.
Rainbows are produced by a combination of refraction and reflection and involve the dispersion of sunlight into a continuous distribution of colors.
Dispersion produces beautiful rainbows but also causes problems in certain optical systems.

Light rays entering a converging lens parallel to its axis cross one another at a single point on the opposite side.
For a converging lens, the focal point is the point at which converging light rays cross; for a diverging lens, the focal point is the point from which diverging light rays appear to originate.
The distance from the center of the lens to its focal point is called the focal length $f$ .
Power $P$ of a lens is defined to be the inverse of its focal length, $P = \frac{1}{f}$ .
A lens that causes the light rays to bend away from its axis is called a diverging lens.
Ray tracing is the technique of graphically determining the paths that light rays take.
The image in which light rays from one point on the object actually cross at the location of the image and can be projected onto a screen, a piece of film, or the retina of an eye is called a real image.
Thin lens equations are $\frac{1}{d_{o}} + \frac{1}{d_{i}} = \frac{1}{f}$ and $\frac{h_{i}}{h_{o}} = - \frac{d_{i}}{d_{o}} = m$ (magnification).
The distance of the image from the center of the lens is called image distance.
An image that is on the same side of the lens as the object and cannot be projected on a screen is called a virtual image.

The characteristics of an image formed by a flat mirror are: (a) The image and object are the same distance from the mirror, (b) The image is a virtual image, and (c) The image is situated behind the mirror.
Image length is half the radius of curvature.
$f = \frac{R}{2}$
A convex mirror is a diverging mirror and forms only one type of image, namely a virtual image.