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# 1: Reflection and Refraction

• 1.1: Introduction
The part of geometric optics that often causes the most difficulty, particularly in getting the right answer for homework or examination problems, is the vexing matter of sign conventions in lens and mirror calculations.
• 1.2: Reflection at a Plane Surface
The law of reflection of light is merely that the angle of reflection r is equal to the angle of incidence r.
• 1.3: Refraction at a Plane Surface
When a ray of light enters a denser medium it is refracted towards the normal in such a manner than the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, this constant being called the refractive index.
• 1.4: Real and Apparent Depth
When we look down into a pool of water from above, the pool looks less deep than it really is.
• 1.5: Reflection and Refraction
When a ray of light encounters an interface between two transparent media, a portion of it is reflected and a portion is refracted, and it is natural to ask, even during an early introduction to the subject, just what fraction is reflected and what fraction is refracted. The answer to this is quite complicated and involves several parameters.
• 1.6: Refraction by a Prism
Prisms are transparent optical elements with flat, polished surfaces that refract light with at least two non-parallel surfaces. Dispersive prisms may be used to break light up into constituent spectral colors.
• 1.7: The Rainbow
Rainbows are meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of multicolored circular arcs. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. Rainbows can be full circles, but observers normally see only an arc formed by illuminated droplets above the ground  and centered on a line from the sun to the observer's eye.
• 1.8: Differential Form of Snell's Law
Snell’s law in the form nsin⁡θ = constant is useful in calculating how a light ray is bent in travelling from one medium to another where there is a discrete change of refractive index. If there is a medium in which the refractive index is changing continuously, a differential form of Snell’s law may be useful.

Thumbnail: The larger the angle to the normal, the smaller is the fraction of light transmitted rather than reflected, until the angle at which total internal reflection occurs. The color of the rays is to help distinguish the rays, and is not meant to indicate any color dependence. (CC BY-SA 3.0; Clément 421138).