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The lines of sight (shown as dashed lines) intersect at a higher position than where the actual rays originated. This causes the pencil to appear higher and the water to appear shallower than it really is. The depth that the water appears to be when viewed from above is known as the apparent depth.
Description: Refraction at the water/air interface and optical density differences account for the "bent pencil" illusion. Date: 23 February 2011, 10:48 (UTC): Source
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, [1] and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
Absorption of light in water. The refractive index of water at 20 °C for visible light is 1.33. [1] The refractive index of normal ice is 1.31 (from List of refractive indices). In general, an index of refraction is a complex number with real and imaginary parts, where the latter indicates the strength of absorption loss at a particular ...
Refraction at interface. Many materials have a well-characterized refractive index, but these indices often depend strongly upon the frequency of light, causing optical dispersion. Standard refractive index measurements are taken at the "yellow doublet" sodium D line, with a wavelength (λ) of 589 nanometers.
As a pencil of light goes through a flat plane of glass, its half-angle changes to θ 2. Due to Snell's law , the numerical aperture remains the same: NA = n 1 sin θ 1 = n 2 sin θ 2 . In optics , the numerical aperture ( NA ) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept ...
A pencil-beam radar A moving or sweeping pencil-beam radar. In optics, a pencil or pencil of rays, also known as a pencil beam or narrow beam, is a geometric construct (pencil of half-lines) used to describe a beam or portion of a beam of electromagnetic radiation or charged particles, typically in the form of a cone or cylinder.
Under ideal conditions, an observer looking up at the water surface from underneath sees a perfectly circular image of the entire above-water hemisphere—from horizon to horizon. Due to refraction at the air/water boundary, Snell's window compresses a 180° angle of view above water to a 97° angle of view below water, similar to the effect of ...