critical angle(redirected from critical angles)
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The Nature of Refraction
The Law of Refraction
The law of refraction relates the angle of incidence (angle between the incident ray and the normal) to the angle of refraction (angle between the refracted ray and the normal). This law, credited to Willebrord Snell, states that the ratio of the sine of the angle of incidence, i, to the sine of the angle of refraction, r, is equal to the ratio of the speed of light in the original medium, vi, to the speed of light in the refracting medium, vr, or sin i/sin r=vi/vr. Snell's law is often stated in terms of the indexes of refraction of the two media rather than the speeds of light in the media. The index of refraction, n, of a transparent medium is a direct measure of its optical density and is equal to the ratio of the speed of light in a vacuum, c, to the speed of light in the medium: n=c/v.
Indexes of refraction are always equal to or greater than 1; for air, n=1.00029; for water, n=1.33. Using indexes of refraction, Snell's law takes the form sin i/sin r=nr /ni, or ni sin i=nr sin r. If the original medium is denser than the refracting medium (ni greater than nr), sin r will be greater than sin i. Thus, there will be some acute angle less than 90° for the incident ray corresponding to an angle of refraction of 90°. This angle of incidence is known as the critical angle. For angles of incidence greater than the critical angle, refraction cannot take place and the incident ray is instead reflected back into the original medium according to the law of reflection (angle of reflection equals angle of incidence). This phenomenon is known as total internal reflection.
Applications of Refraction
critical angle[′krid·ə·kəl ¦aŋ·gəl]
ii. The angle of attack of an airfoil at which the flow of air about the airfoil changes abruptly in such a manner that the lift is sharply reduced and the drag is sharply increased. Sometimes called stalling angle of attack.
iii. The angle at which a reflected ray of light when transmitted from a denser to a rarer medium is bent so far from the normal that it does not enter the rarer medium at all but travels parallel to the surface between the media.
iv. The angle of bank beyond which a helicopter resting on the ground on one skid or one wheel is likely to roll over in an uncontrolled manner.
At the instant of rollover of a helicopter, a moment is produced by the horizontal component of total rotor thrust about the point of ground contact of the skid. This moment is opposed by weight of the aircraft. If the angle of bank is beyond the critical angle the restoring moment is too small to stop the helicopter from rolling over.